It is now evident that the estimation of logistic regression parameters, using Maximum Likelihood... more It is now evident that the estimation of logistic regression parameters, using Maximum Likelihood Estimator (MLE), suffers a huge drawback in the presence of outliers. An alternative approach is to use robust logistic regression estimators, such as Mallows type leverage dependent weights estimator (MALLOWS), Conditionally Unbiased Bounded Influence Function estimator (CUBIF), Bianco and Yohai estimator (BY), and Weighted Bianco and Yohai estimator (WBY). This paper investigates the robustness of the preceding robust estimators by using real data sets and Monte Carlo simulations. The results indicate that the MLE behaves poorly in the presence of outliers. On the other hand, the WBY estimator is more efficient than the other existing robust estimators. Thus, it is suggested that the WBY estimator be employed when outliers are present in the data to obtain a reliable estimate.
Circular data analysis is a particular branch of statistics that sits somewhere between the analy... more Circular data analysis is a particular branch of statistics that sits somewhere between the analysis of linear data and the analysis of spherical data. Circular data are used in many scientific fields. The efficiency of the statistical methods that are applied depends on the accuracy of the data in the study. However, circular data may have outliers that cannot be deleted. If this is the case, we have two ways to avoid the effect of outliers. First, we can apply robust methods for statistical estimations. Second, we can adjust the outliers using the other clean data points in the dataset. In this paper, we focus on adjusting outliers in circular data using the circular distance between the circular data points and the circular mean direction. The proposed procedure is tested by applying it to a simulation study and to real data sets. The results show that the proposed procedure can adjust outliers according to the measures used in the paper.
Circular data analysis is a particular branch of statistics that sits somewhere between the analy... more Circular data analysis is a particular branch of statistics that sits somewhere between the analysis of linear data and the analysis of spherical data. Circular data are used in many scientific fields. The efficiency of the statistical methods that are applied depends on the accuracy of the data in the study. However, circular data may have outliers that cannot be deleted. If this is the case, we have two ways to avoid the effect of outliers. First, we can apply robust methods for statistical estimations. Second, we can adjust the outliers using the other clean data points in the dataset. In this paper, we focus on adjusting outliers in circular data using the circular distance between the circular data points and the circular mean direction. The proposed procedure is tested by applying it to a simulation study and to real data sets. The results show that the proposed procedure can adjust outliers according to the measures used in the paper.
ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, 2021
Identification of spatial outlier is essential in revealing hidden useful knowledge in different ... more Identification of spatial outlier is essential in revealing hidden useful knowledge in different fields of statistical applications for big data. The Score Statistic () has been used as a diagnostic tool for the identification of spatial outliers in big data. Nonetheless, the method suffers from masking and swamping effects. In order to reduce the swamping effect, we propose two methods denoted as and. The and methods adopt location adjacency to construct spatial weights, namely metric distance reciprocal (MDR) weight and exponential weight (EW), respectively, to detect outliers in spatial autoregressiveregressive model (SAR), spatial autoregressive error model (SEM) and general spatial autoregressive-regressive model (GSM). Difference between spatial residuals are calibrated to incorporate adjacency effect into spatial outlier residual. The results of the simulation study and real example show that the performances of the three methods are equally good for SAR model. The and are comparable and both outperform the for SEM and GSM models with less swamping effects and less computational running times.
Journal of Modern Applied Statistical Methods, 2018
The violation of the assumption of homoscedasticity and the presence of high leverage points (HLP... more The violation of the assumption of homoscedasticity and the presence of high leverage points (HLPs) are common in the use of regression models. The weighted least squares can provide the solution to heteroscedastic regression model if the heteroscedastic error structures are known. Based on Furno (1996), two robust weighting methods are proposed based on HLP detection measures (robust Mahalanobis distance based on minimum volume ellipsoid and diagnostic robust generalized potential based on index set equality (DRGP(ISE)) on robust heteroscedasticity consistent covariance matrix estimators. Results obtained from a simulation study and real data sets indicated the DRGP(ISE) method is superior.
Confidence interval is an estimate of a certain parameter. Classical construction of confidence i... more Confidence interval is an estimate of a certain parameter. Classical construction of confidence interval based on asymptotic normality (Wald) often produces misleading inferences when dealing with censored data especially in small samples. Alternative techniques allow us to construct the confidence interval estimation without relying on this assumption. In this paper, we compare the performances of the jackknife and several bootstraps confidence interval estimates for the parameters of a log logistic model with censored data and covariate. We investigate their performances at two nominal error probability levels and several levels of censoring proportion. Conclusions were then drawn based on the results of the coverage probability study.
This article is concerned with the performance of the maximum estimated likelihood estimator in t... more This article is concerned with the performance of the maximum estimated likelihood estimator in the presence of separation in the space of the independent variables and high leverage points. The maximum likelihood estimator suffers from the problem of non overlap cases in the covariates where the regression coefficients are not identifiable and the maximum likelihood estimator does not exist. Consequently, iteration scheme fails to converge and gives faulty results. To remedy this problem, the maximum estimated likelihood estimator is put forward. It is evident that the maximum estimated likelihood estimator is resistant against separation and the estimates always exist. The effect of high leverage points are then investigated on the performance of maximum estimated likelihood estimator through real data sets and Monte Carlo simulation study. The findings signify that the maximum estimated likelihood estimator fails to provide better parameter estimates in the presence of both separation, and high leverage points.
2012 International Conference on Statistics in Science, Business and Engineering (ICSSBE), 2012
ABSTRACT The Ordinary Least Squares (OLS) method is the most widely used method to estimate the p... more ABSTRACT The Ordinary Least Squares (OLS) method is the most widely used method to estimate the parameters of regression model. One of the critical assumption of the OLS estimation method is that the regression variables are measured without error. However, in many practical situations this assumption is often violated, whereby both dependent and independent variables are measured with errors. In these situations the OLS estimates lead to inconsistent and biased estimates. Consequently, the parameter estimates do not come closer to the true values, even in very large sample. To remedy this problem, instrumental variables (IV) estimation technique is utilized. In this article we examine some interesting numerical examples which are related to measurement errors. The results show that the IV estimates is more appropriate than the OLS estimates in such situations.
Nowadays bootstrap techniques are used for data analysis in many other fields like engineering, p... more Nowadays bootstrap techniques are used for data analysis in many other fields like engineering, physics, meteorology, medicine, biology, and chemistry. In this paper, the robustness of Wu (1986) and Liu (1988)'s Wild Bootstrap techniques is examined. The empirical evidences indicate that these techniques yield efficient estimates in the presence of heteroscedasticity problem. However, in the presence of outliers, these estimates are no longer efficient. To remedy this problem, we propose a Robust Wild Bootstrap for stabilizing the variance of the regression estimates where heteroscedasticity and outliers occur at the same time. The proposed method is based on the weighted residuals which incorporate the MM estimator, robust location and scale, and the bootstrap sampling scheme of Wu (1986) and Liu (1988). The results of this study show that the proposed method outperforms the existing ones in every respect.
The support vector regression (SVR) model is currently a very popular non-parametric method used ... more The support vector regression (SVR) model is currently a very popular non-parametric method used for estimating linear and non-linear relationships between response and predictor variables. However, there is a possibility of selecting vertical outliers as support vectors that can unduly affect the estimates of regression. Outliers from abnormal data points may result in bad predictions. In addition, when both vertical outliers and high leverage points are present in the data, the problem is further complicated. In this paper, we introduced a modified robust SVR technique in the simultaneous presence of these two problems. Three types of SVR models, i.e. eps-regression (e-SVR), nu-regression (v-SVR) and bound constraint eps-regression (e-BSVR), with eight different kernel functions are integrated into the new proposed algorithm. Based on 10-fold cross-validation and some model performance measures, the best model with a suitable kernel function is selected. To make the selected model...
Influential observations (IO) are those observations that are responsible for misleading conclusi... more Influential observations (IO) are those observations that are responsible for misleading conclusions about the fitting of a multiple linear regression model. The existing IO identification methods such as influential distance (ID) is not very successful in detecting IO. It is suspected that the ID employed inefficient method with long computational running time for the identification of the suspected IO at the initial step. Moreover, this method declares good leverage observations as IO, resulting in misleading conclusion. In this paper, we proposed fast improvised influential distance (FIID) that can successfully identify IO, good leverage observations, and regular observations with shorter computational running time. Monte Carlo simulation study and real data examples show that the FIID correctly identify genuine IO in multiple linear regression model with no masking and a negligible swamping rate.
Abstract: Problem statement: Most of the statistical procedures heavily depend on normality assum... more Abstract: Problem statement: Most of the statistical procedures heavily depend on normality assumption of observations. In regression, we assumed that the random disturbances were normally distributed. Since the disturbances were unobserved, normality tests were done on regression residuals. But it is now evident that normality tests on residuals suffer from superimposed normality and often possess very poor power. Approach: This study showed that normality tests suffer huge set back in the presence of outliers. We proposed a new robust omnibus test based on rescaled moments and coefficients of skewness and kurtosis of residuals that we call robust rescaled moment test. Results: Numerical examples and Monte Carlo simulations showed that this proposed test performs better than the existing tests for normality in the presence of outliers. Conclusion/Recommendation: We recommend using our proposed omnibus test instead of the existing tests for checking the normality of the regression r...
Quality engineering practitioners have great interest for using response surface method in a real... more Quality engineering practitioners have great interest for using response surface method in a real situation. Recently, dual response surface has been widely used extensively and is known as one powerful tool for robust design. However, existing methods do not consider the information provided by customers and design engineers. One of the methods that can be used to simultaneously optimize multiple responses is by using the desirability function technique. In this technique, the desirability function approach uses a dimensionality reduction approach that converts multiple predicted responses into a single response problem. The traditional procedures construct the process location and process scale based on sample mean and sample variance respectively. Then, for the regression fitting, the Ordinary Least Square (OLS) method is usually used to acquire the sufficient response functions for the process location and scale based on mean and variance. Nevertheless, these existing procedures are easily influenced by outliers. As an alternative, we propose an improvised desirability function for dual response (IDFDR) to rectify this problem. A numerical example is presented to assess the performance of the IDFDR method. The numerical results signify that the IDFDR method is more efficient than the existing methods.
The Ordinary Least Squares (OLS) method is often used to estimate the parameters of a second-orde... more The Ordinary Least Squares (OLS) method is often used to estimate the parameters of a second-order polynomial response surface methodology (RSM) model whereby a face-centered composite design of experiment is considered. The parameters of the model are usually estimated using the OLS technique. Nevertheless, the classical OLS suffers a huge set back in the presence of a typical observations that we often call outliers. In this situation, the optimum response estimator is not reliable as it is based on the OLS which is not resistant to outliers. As an alternative, we propose using a robust MM-estimator to estimate the parameters of the RSM and subsequently the optimum response is determined. A numerical example and simulation study are presented to assess the performance of the optimum response-MM based, denoted as Optimum-MM. The numerical results signify that the Optimum-MM is more efficient than the Optimum-OLS.
This study finds that nominal exchange rate exhibits nonlinear long-run relationship with money s... more This study finds that nominal exchange rate exhibits nonlinear long-run relationship with money supplies and aggregate outputs, in the context of ASEAN-5 countries, thereby validating the monetary model of exchange rate. While it is consistent with the earlier findings using the linear testing procedures in this region, the current evidence of nonlinear relationship provides insightful information in explaining why nominal exchange rate misalignments can sometimes be persistent in the short-run. With regard to the monitoring of exchange rates in these countries, policy makers could focus on the set of monetary variables, which have been shown well-coordinated with the dynamic of exchange rates in this study.
The ordinary least squares (OLS) procedure is inefficient when the underlying assumption of const... more The ordinary least squares (OLS) procedure is inefficient when the underlying assumption of constant error variances (homoscedasticity) is not met. As an alternative, we often used weighted least squares (WLS) procedure which requires a known form of the heteroscedastic errors structures, to estimate the regression parameters when heteroscedasticity occurs in the data. It is now evident that the WLS estimator is easily affected by outliers. To remedy the problem of heteroscedasticity and outliers simultaneously, we proposed a new method that we call two-step robust weighted least squares (TSRWLS) where prior information on the structure of the heteroscedastic errors is not required. The performance of the newly proposed estimator is investigated extensively by real data sets and Monte Carlo simulations.
The Breusch-Godfrey test is widely used for autocorrelation detection. This test is based on the ... more The Breusch-Godfrey test is widely used for autocorrelation detection. This test is based on the OLS estimates. The presence of high leverage points may have an unduly effect on this test. In this paper, we suggest a robust Breusch-Godfrey test which is not easily affected by high leverage points. The results of the study shows that the robustified Breusch-Godfrey test consistently detect the autocorrelation problem with and without the presence of high leverage points in two independents variables of multiple regression.
Outliers in the X-direction or high leverage points are the latest known source of multicollinear... more Outliers in the X-direction or high leverage points are the latest known source of multicollinearity. Multicollinearity is a nonorthogonality of two or more explanatory variables in multiple regression models, which may have important influential impacts on interpreting a fitted regression model. In this paper, we performed Monte Carlo simulation studies to achieve two main objectives. The first objective was to study the effect of certain magnitude and percentage of high leverage points, which are two important issues in tending the high leverage points to be collinearity-enhancing observations, on the multicollinarity pattern of the data. The second objective was to investigate in which situations these points do make different degrees of multicollinearity, such as moderate or severe. According to the simulation results, high leverage points should be in large magnitude for at least two explanatory variables to guarantee that they are the cause of multicollinearity problems. We al...
International journal of applied mathematics and statistics, 2014
Influence diagnostics are essential in statistical modeling as the influential points have large ... more Influence diagnostics are essential in statistical modeling as the influential points have large effect on any statistical model. Thus, in this article, the identification of influential points in Cox proportional hazards model is considered. There are several diagnostics approaches in Cox proportional hazards model; these approaches are: score residual, scaled score residual, Lmax statistics, and likelihood displacement. We also propose a new diagnostics approach and compare its performance with the existing ones. It is found that the new proposed influential detection performs equally with the existing methods; it works to identify the influential observation.
It is now evident that the estimation of logistic regression parameters, using Maximum Likelihood... more It is now evident that the estimation of logistic regression parameters, using Maximum Likelihood Estimator (MLE), suffers a huge drawback in the presence of outliers. An alternative approach is to use robust logistic regression estimators, such as Mallows type leverage dependent weights estimator (MALLOWS), Conditionally Unbiased Bounded Influence Function estimator (CUBIF), Bianco and Yohai estimator (BY), and Weighted Bianco and Yohai estimator (WBY). This paper investigates the robustness of the preceding robust estimators by using real data sets and Monte Carlo simulations. The results indicate that the MLE behaves poorly in the presence of outliers. On the other hand, the WBY estimator is more efficient than the other existing robust estimators. Thus, it is suggested that the WBY estimator be employed when outliers are present in the data to obtain a reliable estimate.
Circular data analysis is a particular branch of statistics that sits somewhere between the analy... more Circular data analysis is a particular branch of statistics that sits somewhere between the analysis of linear data and the analysis of spherical data. Circular data are used in many scientific fields. The efficiency of the statistical methods that are applied depends on the accuracy of the data in the study. However, circular data may have outliers that cannot be deleted. If this is the case, we have two ways to avoid the effect of outliers. First, we can apply robust methods for statistical estimations. Second, we can adjust the outliers using the other clean data points in the dataset. In this paper, we focus on adjusting outliers in circular data using the circular distance between the circular data points and the circular mean direction. The proposed procedure is tested by applying it to a simulation study and to real data sets. The results show that the proposed procedure can adjust outliers according to the measures used in the paper.
Circular data analysis is a particular branch of statistics that sits somewhere between the analy... more Circular data analysis is a particular branch of statistics that sits somewhere between the analysis of linear data and the analysis of spherical data. Circular data are used in many scientific fields. The efficiency of the statistical methods that are applied depends on the accuracy of the data in the study. However, circular data may have outliers that cannot be deleted. If this is the case, we have two ways to avoid the effect of outliers. First, we can apply robust methods for statistical estimations. Second, we can adjust the outliers using the other clean data points in the dataset. In this paper, we focus on adjusting outliers in circular data using the circular distance between the circular data points and the circular mean direction. The proposed procedure is tested by applying it to a simulation study and to real data sets. The results show that the proposed procedure can adjust outliers according to the measures used in the paper.
ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, 2021
Identification of spatial outlier is essential in revealing hidden useful knowledge in different ... more Identification of spatial outlier is essential in revealing hidden useful knowledge in different fields of statistical applications for big data. The Score Statistic () has been used as a diagnostic tool for the identification of spatial outliers in big data. Nonetheless, the method suffers from masking and swamping effects. In order to reduce the swamping effect, we propose two methods denoted as and. The and methods adopt location adjacency to construct spatial weights, namely metric distance reciprocal (MDR) weight and exponential weight (EW), respectively, to detect outliers in spatial autoregressiveregressive model (SAR), spatial autoregressive error model (SEM) and general spatial autoregressive-regressive model (GSM). Difference between spatial residuals are calibrated to incorporate adjacency effect into spatial outlier residual. The results of the simulation study and real example show that the performances of the three methods are equally good for SAR model. The and are comparable and both outperform the for SEM and GSM models with less swamping effects and less computational running times.
Journal of Modern Applied Statistical Methods, 2018
The violation of the assumption of homoscedasticity and the presence of high leverage points (HLP... more The violation of the assumption of homoscedasticity and the presence of high leverage points (HLPs) are common in the use of regression models. The weighted least squares can provide the solution to heteroscedastic regression model if the heteroscedastic error structures are known. Based on Furno (1996), two robust weighting methods are proposed based on HLP detection measures (robust Mahalanobis distance based on minimum volume ellipsoid and diagnostic robust generalized potential based on index set equality (DRGP(ISE)) on robust heteroscedasticity consistent covariance matrix estimators. Results obtained from a simulation study and real data sets indicated the DRGP(ISE) method is superior.
Confidence interval is an estimate of a certain parameter. Classical construction of confidence i... more Confidence interval is an estimate of a certain parameter. Classical construction of confidence interval based on asymptotic normality (Wald) often produces misleading inferences when dealing with censored data especially in small samples. Alternative techniques allow us to construct the confidence interval estimation without relying on this assumption. In this paper, we compare the performances of the jackknife and several bootstraps confidence interval estimates for the parameters of a log logistic model with censored data and covariate. We investigate their performances at two nominal error probability levels and several levels of censoring proportion. Conclusions were then drawn based on the results of the coverage probability study.
This article is concerned with the performance of the maximum estimated likelihood estimator in t... more This article is concerned with the performance of the maximum estimated likelihood estimator in the presence of separation in the space of the independent variables and high leverage points. The maximum likelihood estimator suffers from the problem of non overlap cases in the covariates where the regression coefficients are not identifiable and the maximum likelihood estimator does not exist. Consequently, iteration scheme fails to converge and gives faulty results. To remedy this problem, the maximum estimated likelihood estimator is put forward. It is evident that the maximum estimated likelihood estimator is resistant against separation and the estimates always exist. The effect of high leverage points are then investigated on the performance of maximum estimated likelihood estimator through real data sets and Monte Carlo simulation study. The findings signify that the maximum estimated likelihood estimator fails to provide better parameter estimates in the presence of both separation, and high leverage points.
2012 International Conference on Statistics in Science, Business and Engineering (ICSSBE), 2012
ABSTRACT The Ordinary Least Squares (OLS) method is the most widely used method to estimate the p... more ABSTRACT The Ordinary Least Squares (OLS) method is the most widely used method to estimate the parameters of regression model. One of the critical assumption of the OLS estimation method is that the regression variables are measured without error. However, in many practical situations this assumption is often violated, whereby both dependent and independent variables are measured with errors. In these situations the OLS estimates lead to inconsistent and biased estimates. Consequently, the parameter estimates do not come closer to the true values, even in very large sample. To remedy this problem, instrumental variables (IV) estimation technique is utilized. In this article we examine some interesting numerical examples which are related to measurement errors. The results show that the IV estimates is more appropriate than the OLS estimates in such situations.
Nowadays bootstrap techniques are used for data analysis in many other fields like engineering, p... more Nowadays bootstrap techniques are used for data analysis in many other fields like engineering, physics, meteorology, medicine, biology, and chemistry. In this paper, the robustness of Wu (1986) and Liu (1988)'s Wild Bootstrap techniques is examined. The empirical evidences indicate that these techniques yield efficient estimates in the presence of heteroscedasticity problem. However, in the presence of outliers, these estimates are no longer efficient. To remedy this problem, we propose a Robust Wild Bootstrap for stabilizing the variance of the regression estimates where heteroscedasticity and outliers occur at the same time. The proposed method is based on the weighted residuals which incorporate the MM estimator, robust location and scale, and the bootstrap sampling scheme of Wu (1986) and Liu (1988). The results of this study show that the proposed method outperforms the existing ones in every respect.
The support vector regression (SVR) model is currently a very popular non-parametric method used ... more The support vector regression (SVR) model is currently a very popular non-parametric method used for estimating linear and non-linear relationships between response and predictor variables. However, there is a possibility of selecting vertical outliers as support vectors that can unduly affect the estimates of regression. Outliers from abnormal data points may result in bad predictions. In addition, when both vertical outliers and high leverage points are present in the data, the problem is further complicated. In this paper, we introduced a modified robust SVR technique in the simultaneous presence of these two problems. Three types of SVR models, i.e. eps-regression (e-SVR), nu-regression (v-SVR) and bound constraint eps-regression (e-BSVR), with eight different kernel functions are integrated into the new proposed algorithm. Based on 10-fold cross-validation and some model performance measures, the best model with a suitable kernel function is selected. To make the selected model...
Influential observations (IO) are those observations that are responsible for misleading conclusi... more Influential observations (IO) are those observations that are responsible for misleading conclusions about the fitting of a multiple linear regression model. The existing IO identification methods such as influential distance (ID) is not very successful in detecting IO. It is suspected that the ID employed inefficient method with long computational running time for the identification of the suspected IO at the initial step. Moreover, this method declares good leverage observations as IO, resulting in misleading conclusion. In this paper, we proposed fast improvised influential distance (FIID) that can successfully identify IO, good leverage observations, and regular observations with shorter computational running time. Monte Carlo simulation study and real data examples show that the FIID correctly identify genuine IO in multiple linear regression model with no masking and a negligible swamping rate.
Abstract: Problem statement: Most of the statistical procedures heavily depend on normality assum... more Abstract: Problem statement: Most of the statistical procedures heavily depend on normality assumption of observations. In regression, we assumed that the random disturbances were normally distributed. Since the disturbances were unobserved, normality tests were done on regression residuals. But it is now evident that normality tests on residuals suffer from superimposed normality and often possess very poor power. Approach: This study showed that normality tests suffer huge set back in the presence of outliers. We proposed a new robust omnibus test based on rescaled moments and coefficients of skewness and kurtosis of residuals that we call robust rescaled moment test. Results: Numerical examples and Monte Carlo simulations showed that this proposed test performs better than the existing tests for normality in the presence of outliers. Conclusion/Recommendation: We recommend using our proposed omnibus test instead of the existing tests for checking the normality of the regression r...
Quality engineering practitioners have great interest for using response surface method in a real... more Quality engineering practitioners have great interest for using response surface method in a real situation. Recently, dual response surface has been widely used extensively and is known as one powerful tool for robust design. However, existing methods do not consider the information provided by customers and design engineers. One of the methods that can be used to simultaneously optimize multiple responses is by using the desirability function technique. In this technique, the desirability function approach uses a dimensionality reduction approach that converts multiple predicted responses into a single response problem. The traditional procedures construct the process location and process scale based on sample mean and sample variance respectively. Then, for the regression fitting, the Ordinary Least Square (OLS) method is usually used to acquire the sufficient response functions for the process location and scale based on mean and variance. Nevertheless, these existing procedures are easily influenced by outliers. As an alternative, we propose an improvised desirability function for dual response (IDFDR) to rectify this problem. A numerical example is presented to assess the performance of the IDFDR method. The numerical results signify that the IDFDR method is more efficient than the existing methods.
The Ordinary Least Squares (OLS) method is often used to estimate the parameters of a second-orde... more The Ordinary Least Squares (OLS) method is often used to estimate the parameters of a second-order polynomial response surface methodology (RSM) model whereby a face-centered composite design of experiment is considered. The parameters of the model are usually estimated using the OLS technique. Nevertheless, the classical OLS suffers a huge set back in the presence of a typical observations that we often call outliers. In this situation, the optimum response estimator is not reliable as it is based on the OLS which is not resistant to outliers. As an alternative, we propose using a robust MM-estimator to estimate the parameters of the RSM and subsequently the optimum response is determined. A numerical example and simulation study are presented to assess the performance of the optimum response-MM based, denoted as Optimum-MM. The numerical results signify that the Optimum-MM is more efficient than the Optimum-OLS.
This study finds that nominal exchange rate exhibits nonlinear long-run relationship with money s... more This study finds that nominal exchange rate exhibits nonlinear long-run relationship with money supplies and aggregate outputs, in the context of ASEAN-5 countries, thereby validating the monetary model of exchange rate. While it is consistent with the earlier findings using the linear testing procedures in this region, the current evidence of nonlinear relationship provides insightful information in explaining why nominal exchange rate misalignments can sometimes be persistent in the short-run. With regard to the monitoring of exchange rates in these countries, policy makers could focus on the set of monetary variables, which have been shown well-coordinated with the dynamic of exchange rates in this study.
The ordinary least squares (OLS) procedure is inefficient when the underlying assumption of const... more The ordinary least squares (OLS) procedure is inefficient when the underlying assumption of constant error variances (homoscedasticity) is not met. As an alternative, we often used weighted least squares (WLS) procedure which requires a known form of the heteroscedastic errors structures, to estimate the regression parameters when heteroscedasticity occurs in the data. It is now evident that the WLS estimator is easily affected by outliers. To remedy the problem of heteroscedasticity and outliers simultaneously, we proposed a new method that we call two-step robust weighted least squares (TSRWLS) where prior information on the structure of the heteroscedastic errors is not required. The performance of the newly proposed estimator is investigated extensively by real data sets and Monte Carlo simulations.
The Breusch-Godfrey test is widely used for autocorrelation detection. This test is based on the ... more The Breusch-Godfrey test is widely used for autocorrelation detection. This test is based on the OLS estimates. The presence of high leverage points may have an unduly effect on this test. In this paper, we suggest a robust Breusch-Godfrey test which is not easily affected by high leverage points. The results of the study shows that the robustified Breusch-Godfrey test consistently detect the autocorrelation problem with and without the presence of high leverage points in two independents variables of multiple regression.
Outliers in the X-direction or high leverage points are the latest known source of multicollinear... more Outliers in the X-direction or high leverage points are the latest known source of multicollinearity. Multicollinearity is a nonorthogonality of two or more explanatory variables in multiple regression models, which may have important influential impacts on interpreting a fitted regression model. In this paper, we performed Monte Carlo simulation studies to achieve two main objectives. The first objective was to study the effect of certain magnitude and percentage of high leverage points, which are two important issues in tending the high leverage points to be collinearity-enhancing observations, on the multicollinarity pattern of the data. The second objective was to investigate in which situations these points do make different degrees of multicollinearity, such as moderate or severe. According to the simulation results, high leverage points should be in large magnitude for at least two explanatory variables to guarantee that they are the cause of multicollinearity problems. We al...
International journal of applied mathematics and statistics, 2014
Influence diagnostics are essential in statistical modeling as the influential points have large ... more Influence diagnostics are essential in statistical modeling as the influential points have large effect on any statistical model. Thus, in this article, the identification of influential points in Cox proportional hazards model is considered. There are several diagnostics approaches in Cox proportional hazards model; these approaches are: score residual, scaled score residual, Lmax statistics, and likelihood displacement. We also propose a new diagnostics approach and compare its performance with the existing ones. It is found that the new proposed influential detection performs equally with the existing methods; it works to identify the influential observation.
Uploads
Papers by Habshah Midi