In this paper we study uniform versions of two limit theorems in random left truncation model (RL... more In this paper we study uniform versions of two limit theorems in random left truncation model (RLTM). The law of large numbers (LLN) and the central limit theorem (CLT) have been obtained under the bracketing entropy conditions in this setting. The uniform LLN and the uniform CLT of the present paper extend the one dimensional LLN and the one dimensional CLT under RLTM respectively.
Kernel density estimators are the basic tools for density estimation in nonparametric statistics.... more Kernel density estimators are the basic tools for density estimation in nonparametric statistics. The k-nearest neighbor kernel estimators represent a special form of kernel density estimators, in which the bandwidth is varied depending on the location of the sample points. In this paperwe initially introduce the knearest neighbor kernel density estimator in the random left-truncation model, and then prove some of its asymptotic behaviors, such as strong uniform consistency and asymptotic normality. particularshow that the proposed estimator has truncation-free varianceare presented to illustrate the results and show how the estimator behaves for finite samplesMoreover, the proposed estimator is used to estimate the density function of a real data set.
In this paper we derive a Berry-Esseen type bound for the kernel density estimator of a random le... more In this paper we derive a Berry-Esseen type bound for the kernel density estimator of a random left truncated model, in which each datum (Y) is randomly left truncated and is sampled if Y ≥ T, where T is the truncation random variable with an unknown distribution. This unknown distribution is estimated with the Lynden-Bell estimator. In particular the normal approximation rate, by choice of the bandwidth, is shown to be close to n −1/6 modulo logarithmic term. We have also investigated this normal approximation rate via a simulation study.
In this paper, the distributed estimation in wireless sensor network using optimal task schedulin... more In this paper, the distributed estimation in wireless sensor network using optimal task scheduling is considered. The main goal is to maximize network lifetime where it consists of a fusion center and a set of sensor nodes. Lifetime defined as the number of rounds accomplished before network becomes nonfunctional. In order to prolong network lifetime, we determine the optimal number of active sensor nodes and the number of samples provided by each of them using linear optimization problem. Sensor observations are quantized into messages and then forwarded to a fusion center where a final estimation is performed based on degree of certainty. Simulation results show that our optimal proposed algorithm has achieved significant efficiency when compared with other heuristic methods.
The computational solution of large scale linear programming problems contains various difficulti... more The computational solution of large scale linear programming problems contains various difficulties. One of the difficulties is to ensure numerical stability. There is another difficulty of a different nature, namely the original data, contains errors as well. In this paper, we show that the effect of the random errors in the original data has a diminishing tendency for the optimal value as the number of constraints and the number of variables increase. The laws of large numbers in probability theory are mathematical formulations for indicating the slowing-down tendency of the effect of random errors in the data. This paper was inspired by the paper of Prekopa [3]. Prekopa [3] proved both weak and strong laws of large numbers for the random linear programs in independence setting. We obtain laws of large numbers under negatively associated dependence for random linear programs and we extend Prekopa's results [3] to the case of negatively associated random variables.
In some long-term studies, a series of dependent and possibly censored failure times may be obser... more In some long-term studies, a series of dependent and possibly censored failure times may be observed. Suppose that the failure times have a common continuous distribution function F. A popular stochastic measure of the distance between the density function f of the failure times and its kernel estimate f n is the integrated square error(ISE). In this article, we derive a central limit theorem for the integrated square error of the kernel density estimators under a censored dependent model.
In this article, we consider the product-limit quantile estimator of an unknown quantile function... more In this article, we consider the product-limit quantile estimator of an unknown quantile function under a censored dependent model. This is a parallel problem to the estimation of the unknown distribution function by the product-limit estimator under the same model. Simultaneous strong Gaussian approximations of the product-limit process and product-limit quantile process are constructed with rate O[(log n)−λ] for some λ > 0. The strong Gaussian approximation of the product-limit process is then applied to derive the laws of the iterated logarithm for product-limit process.
In this paper, the distributed estimation in Wire less Sensor Network (WSN) using optimal task sc... more In this paper, the distributed estimation in Wire less Sensor Network (WSN) using optimal task scheduling is looked upon. The main goal is to prolong network lifetime while the target parameter is estimated with desirable precision. The lifetime is defined as the number of rounds accomplished before network becomes nonfunctional. In order to prolong network lifetime, we determine the optimal number of active sensor nodes and the number of samples provided by each of them ba sed on the degree of certainty (u tilizing linear programming). Sensor observations from environment are quanti zed into messages and then directly for warded to a fusion center where a final estimation is performed. Simulation results confirm that our optimal proposed algorithm has achieved significant efficiency when compared with other heuristic methods.
Background Road traffic law enforcement was implemented on 1 st April 2011 (the first interventio... more Background Road traffic law enforcement was implemented on 1 st April 2011 (the first intervention) and traffic ticket fines have been increased on 1 st March 2016 (the second intervention) in Iran. The aim of the current study was to evaluate the effects of the law enforcement on reduction in the incidence rate of road traffic fatality (IRRTF), the incidence rate of road traffic injuries (IRRTI) and the incidence rate of rural road traffic offenses (IRRRTO) in Iran. Methods Interrupted time series analysis was conducted to evaluate the impact of law enforcement and increased traffic tickets fines. Monthly data of fatality on urban, rural and local rural roads, injuries with respect to gender and traffic offenses namely speeding, illegal overtaking and tailgating were investigated separately for the period 2009-2016. Results Results showed a reduction in the incidence rate of total road traffic fatality (IRTRTF), the incidence rate of rural road traffic fatality (IRRRTF) and the incidence rate of urban road traffic fatality (IRURTF) by-21.44% (-39.3 to-3.59, 95% CI),-21.25% (-31.32 to-11.88, 95% CI) and-26.75% (-37.49 to-16, 95% CI) through the first intervention which resulted in 0.383, 0.255 and 0.222 decline in casualties per 100 000 population, respectively. Conversely, no reduction was found in the incidence rate of local rural road traffic fatality (IRLRRTF) and the IRRTI. Second intervention was found to only affect the IRURTF with-26.75% (-37.49 to-16, 95% CI) which led to 0.222 casualties per 100 000 population. In addition, a reduction effect was observed on the incidence rate of illegal overtaking (IRIO) and the incidence rate of speeding (IRS) with-42.8% (-57.39 to-28.22, 95% CI) and-10.54% (-21.05 to-0.03, 95% CI which implied a decrease of 415.85 and 1003.8 in monthly traffic offenses per 100 000 vehicles), respectively.
In this paper, the distributed estimation in wireless sensor network using optimal task schedulin... more In this paper, the distributed estimation in wireless sensor network using optimal task scheduling is considered. The main goal is to maximize network lifetime where it consists of a fusion center and a set of sensor nodes. Lifetime defined as the number of rounds accomplished before network becomes nonfunctional. In order to prolong network lifetime, we determine the optimal number of active sensor nodes and the number of samples provided by each of them using linear optimization problem. Sensor observations are quantized into messages and then forwarded to a fusion center where a final estimation is performed based on degree of certainty. Simulation results show that our optimal proposed algorithm has achieved significant efficiency when compared with other heuristic methods.
In this paper, we consider the kernel-type estimator of the quantile function based on the kernel... more In this paper, we consider the kernel-type estimator of the quantile function based on the kernel smoother under a censored dependent model. The Bahadur-type representation of the kernel smooth estimator is established, and from the Bahadur representation we can show that this estimator is strongly consistent.
Problems with truncated data arise frequently in survival analyses and reliability applications. ... more Problems with truncated data arise frequently in survival analyses and reliability applications. The estimation of the density function of the lifetimes is often of interest. In this article, the estimation of density function by the kernel method is considered, when ...
In this article, we propose two non-parametric estimators for the past entropy based on length-bi... more In this article, we propose two non-parametric estimators for the past entropy based on length-biased data and the strong consistency of the proposed estimators is proved. In addition, some simulations are conducted to evaluate the performance of the proposed estimators. Based on the results, we show that they have better performance in a different region of the probability distribution for length biased random variables.
Background Road traffic law enforcement was implemented on 1 st April 2011 (the first interventio... more Background Road traffic law enforcement was implemented on 1 st April 2011 (the first intervention) and traffic ticket fines have been increased on 1 st March 2016 (the second intervention) in Iran. The aim of the current study was to evaluate the effects of the law enforcement on reduction in the incidence rate of road traffic fatality (IRRTF), the incidence rate of road traffic injuries (IRRTI) and the incidence rate of rural road traffic offenses (IRRRTO) in Iran. Methods Interrupted time series analysis was conducted to evaluate the impact of law enforcement and increased traffic tickets fines. Monthly data of fatality on urban, rural and local rural roads, injuries with respect to gender and traffic offenses namely speeding, illegal overtaking and tailgating were investigated separately for the period 2009-2016. Results Results showed a reduction in the incidence rate of total road traffic fatality (IRTRTF), the incidence rate of rural road traffic fatality (IRRRTF) and the incidence rate of urban road traffic fatality (IRURTF) by-21.44% (-39.3 to-3.59, 95% CI),-21.25% (-31.32 to-11.88, 95% CI) and-26.75% (-37.49 to-16, 95% CI) through the first intervention which resulted in 0.383, 0.255 and 0.222 decline in casualties per 100 000 population, respectively. Conversely, no reduction was found in the incidence rate of local rural road traffic fatality (IRLRRTF) and the IRRTI. Second intervention was found to only affect the IRURTF with-26.75% (-37.49 to-16, 95% CI) which led to 0.222 casualties per 100 000 population. In addition, a reduction effect was observed on the incidence rate of illegal overtaking (IRIO) and the incidence rate of speeding (IRS) with-42.8% (-57.39 to-28.22, 95% CI) and-10.54% (-21.05 to-0.03, 95% CI which implied a decrease of 415.85 and 1003.8 in monthly traffic offenses per 100 000 vehicles), respectively.
Pakistan Journal of Statistics and Operation Research
In this paper, we introduce some new goodness-of-fit tests for the Rayleigh distribution based on... more In this paper, we introduce some new goodness-of-fit tests for the Rayleigh distribution based on Jeffreys, Lin-Wong and Renyi divergence measures. Then, the new proposed tests are compared with other tests in the literature. We compare the power of considered tests for some alternative distributions whose powers are calculated by Monte Carlo simulation. Finally, we conclude that entropy-based tests have a good performance in terms of power and among them Jeffreys test is the best one.
In this paper, we propose a test for the null hypothesis that a decreasing density function belon... more In this paper, we propose a test for the null hypothesis that a decreasing density function belongs to a givenparametric family of distribution functions against the non-parametric alternative. This method, which is based on an empirical likelihood (EL) ratio statistic, is similar to the test introduced by Vexler and Gurevich [23]. The consistency of the test statistic proposed is derived under the null and alternative hypotheses. A simulation study is conducted to inspect the power of the proposed test under various decreasing alternatives. In each scenario, the critical region of the test is obtained using a Monte Carlo technique. The applicability of the proposed test in practice is demonstrated through a few real data examples.
In this paper we study uniform versions of two limit theorems in random left truncation model (RL... more In this paper we study uniform versions of two limit theorems in random left truncation model (RLTM). The law of large numbers (LLN) and the central limit theorem (CLT) have been obtained under the bracketing entropy conditions in this setting. The uniform LLN and the uniform CLT of the present paper extend the one dimensional LLN and the one dimensional CLT under RLTM respectively.
Kernel density estimators are the basic tools for density estimation in nonparametric statistics.... more Kernel density estimators are the basic tools for density estimation in nonparametric statistics. The k-nearest neighbor kernel estimators represent a special form of kernel density estimators, in which the bandwidth is varied depending on the location of the sample points. In this paperwe initially introduce the knearest neighbor kernel density estimator in the random left-truncation model, and then prove some of its asymptotic behaviors, such as strong uniform consistency and asymptotic normality. particularshow that the proposed estimator has truncation-free varianceare presented to illustrate the results and show how the estimator behaves for finite samplesMoreover, the proposed estimator is used to estimate the density function of a real data set.
In this paper we derive a Berry-Esseen type bound for the kernel density estimator of a random le... more In this paper we derive a Berry-Esseen type bound for the kernel density estimator of a random left truncated model, in which each datum (Y) is randomly left truncated and is sampled if Y ≥ T, where T is the truncation random variable with an unknown distribution. This unknown distribution is estimated with the Lynden-Bell estimator. In particular the normal approximation rate, by choice of the bandwidth, is shown to be close to n −1/6 modulo logarithmic term. We have also investigated this normal approximation rate via a simulation study.
In this paper, the distributed estimation in wireless sensor network using optimal task schedulin... more In this paper, the distributed estimation in wireless sensor network using optimal task scheduling is considered. The main goal is to maximize network lifetime where it consists of a fusion center and a set of sensor nodes. Lifetime defined as the number of rounds accomplished before network becomes nonfunctional. In order to prolong network lifetime, we determine the optimal number of active sensor nodes and the number of samples provided by each of them using linear optimization problem. Sensor observations are quantized into messages and then forwarded to a fusion center where a final estimation is performed based on degree of certainty. Simulation results show that our optimal proposed algorithm has achieved significant efficiency when compared with other heuristic methods.
The computational solution of large scale linear programming problems contains various difficulti... more The computational solution of large scale linear programming problems contains various difficulties. One of the difficulties is to ensure numerical stability. There is another difficulty of a different nature, namely the original data, contains errors as well. In this paper, we show that the effect of the random errors in the original data has a diminishing tendency for the optimal value as the number of constraints and the number of variables increase. The laws of large numbers in probability theory are mathematical formulations for indicating the slowing-down tendency of the effect of random errors in the data. This paper was inspired by the paper of Prekopa [3]. Prekopa [3] proved both weak and strong laws of large numbers for the random linear programs in independence setting. We obtain laws of large numbers under negatively associated dependence for random linear programs and we extend Prekopa's results [3] to the case of negatively associated random variables.
In some long-term studies, a series of dependent and possibly censored failure times may be obser... more In some long-term studies, a series of dependent and possibly censored failure times may be observed. Suppose that the failure times have a common continuous distribution function F. A popular stochastic measure of the distance between the density function f of the failure times and its kernel estimate f n is the integrated square error(ISE). In this article, we derive a central limit theorem for the integrated square error of the kernel density estimators under a censored dependent model.
In this article, we consider the product-limit quantile estimator of an unknown quantile function... more In this article, we consider the product-limit quantile estimator of an unknown quantile function under a censored dependent model. This is a parallel problem to the estimation of the unknown distribution function by the product-limit estimator under the same model. Simultaneous strong Gaussian approximations of the product-limit process and product-limit quantile process are constructed with rate O[(log n)−λ] for some λ > 0. The strong Gaussian approximation of the product-limit process is then applied to derive the laws of the iterated logarithm for product-limit process.
In this paper, the distributed estimation in Wire less Sensor Network (WSN) using optimal task sc... more In this paper, the distributed estimation in Wire less Sensor Network (WSN) using optimal task scheduling is looked upon. The main goal is to prolong network lifetime while the target parameter is estimated with desirable precision. The lifetime is defined as the number of rounds accomplished before network becomes nonfunctional. In order to prolong network lifetime, we determine the optimal number of active sensor nodes and the number of samples provided by each of them ba sed on the degree of certainty (u tilizing linear programming). Sensor observations from environment are quanti zed into messages and then directly for warded to a fusion center where a final estimation is performed. Simulation results confirm that our optimal proposed algorithm has achieved significant efficiency when compared with other heuristic methods.
Background Road traffic law enforcement was implemented on 1 st April 2011 (the first interventio... more Background Road traffic law enforcement was implemented on 1 st April 2011 (the first intervention) and traffic ticket fines have been increased on 1 st March 2016 (the second intervention) in Iran. The aim of the current study was to evaluate the effects of the law enforcement on reduction in the incidence rate of road traffic fatality (IRRTF), the incidence rate of road traffic injuries (IRRTI) and the incidence rate of rural road traffic offenses (IRRRTO) in Iran. Methods Interrupted time series analysis was conducted to evaluate the impact of law enforcement and increased traffic tickets fines. Monthly data of fatality on urban, rural and local rural roads, injuries with respect to gender and traffic offenses namely speeding, illegal overtaking and tailgating were investigated separately for the period 2009-2016. Results Results showed a reduction in the incidence rate of total road traffic fatality (IRTRTF), the incidence rate of rural road traffic fatality (IRRRTF) and the incidence rate of urban road traffic fatality (IRURTF) by-21.44% (-39.3 to-3.59, 95% CI),-21.25% (-31.32 to-11.88, 95% CI) and-26.75% (-37.49 to-16, 95% CI) through the first intervention which resulted in 0.383, 0.255 and 0.222 decline in casualties per 100 000 population, respectively. Conversely, no reduction was found in the incidence rate of local rural road traffic fatality (IRLRRTF) and the IRRTI. Second intervention was found to only affect the IRURTF with-26.75% (-37.49 to-16, 95% CI) which led to 0.222 casualties per 100 000 population. In addition, a reduction effect was observed on the incidence rate of illegal overtaking (IRIO) and the incidence rate of speeding (IRS) with-42.8% (-57.39 to-28.22, 95% CI) and-10.54% (-21.05 to-0.03, 95% CI which implied a decrease of 415.85 and 1003.8 in monthly traffic offenses per 100 000 vehicles), respectively.
In this paper, the distributed estimation in wireless sensor network using optimal task schedulin... more In this paper, the distributed estimation in wireless sensor network using optimal task scheduling is considered. The main goal is to maximize network lifetime where it consists of a fusion center and a set of sensor nodes. Lifetime defined as the number of rounds accomplished before network becomes nonfunctional. In order to prolong network lifetime, we determine the optimal number of active sensor nodes and the number of samples provided by each of them using linear optimization problem. Sensor observations are quantized into messages and then forwarded to a fusion center where a final estimation is performed based on degree of certainty. Simulation results show that our optimal proposed algorithm has achieved significant efficiency when compared with other heuristic methods.
In this paper, we consider the kernel-type estimator of the quantile function based on the kernel... more In this paper, we consider the kernel-type estimator of the quantile function based on the kernel smoother under a censored dependent model. The Bahadur-type representation of the kernel smooth estimator is established, and from the Bahadur representation we can show that this estimator is strongly consistent.
Problems with truncated data arise frequently in survival analyses and reliability applications. ... more Problems with truncated data arise frequently in survival analyses and reliability applications. The estimation of the density function of the lifetimes is often of interest. In this article, the estimation of density function by the kernel method is considered, when ...
In this article, we propose two non-parametric estimators for the past entropy based on length-bi... more In this article, we propose two non-parametric estimators for the past entropy based on length-biased data and the strong consistency of the proposed estimators is proved. In addition, some simulations are conducted to evaluate the performance of the proposed estimators. Based on the results, we show that they have better performance in a different region of the probability distribution for length biased random variables.
Background Road traffic law enforcement was implemented on 1 st April 2011 (the first interventio... more Background Road traffic law enforcement was implemented on 1 st April 2011 (the first intervention) and traffic ticket fines have been increased on 1 st March 2016 (the second intervention) in Iran. The aim of the current study was to evaluate the effects of the law enforcement on reduction in the incidence rate of road traffic fatality (IRRTF), the incidence rate of road traffic injuries (IRRTI) and the incidence rate of rural road traffic offenses (IRRRTO) in Iran. Methods Interrupted time series analysis was conducted to evaluate the impact of law enforcement and increased traffic tickets fines. Monthly data of fatality on urban, rural and local rural roads, injuries with respect to gender and traffic offenses namely speeding, illegal overtaking and tailgating were investigated separately for the period 2009-2016. Results Results showed a reduction in the incidence rate of total road traffic fatality (IRTRTF), the incidence rate of rural road traffic fatality (IRRRTF) and the incidence rate of urban road traffic fatality (IRURTF) by-21.44% (-39.3 to-3.59, 95% CI),-21.25% (-31.32 to-11.88, 95% CI) and-26.75% (-37.49 to-16, 95% CI) through the first intervention which resulted in 0.383, 0.255 and 0.222 decline in casualties per 100 000 population, respectively. Conversely, no reduction was found in the incidence rate of local rural road traffic fatality (IRLRRTF) and the IRRTI. Second intervention was found to only affect the IRURTF with-26.75% (-37.49 to-16, 95% CI) which led to 0.222 casualties per 100 000 population. In addition, a reduction effect was observed on the incidence rate of illegal overtaking (IRIO) and the incidence rate of speeding (IRS) with-42.8% (-57.39 to-28.22, 95% CI) and-10.54% (-21.05 to-0.03, 95% CI which implied a decrease of 415.85 and 1003.8 in monthly traffic offenses per 100 000 vehicles), respectively.
Pakistan Journal of Statistics and Operation Research
In this paper, we introduce some new goodness-of-fit tests for the Rayleigh distribution based on... more In this paper, we introduce some new goodness-of-fit tests for the Rayleigh distribution based on Jeffreys, Lin-Wong and Renyi divergence measures. Then, the new proposed tests are compared with other tests in the literature. We compare the power of considered tests for some alternative distributions whose powers are calculated by Monte Carlo simulation. Finally, we conclude that entropy-based tests have a good performance in terms of power and among them Jeffreys test is the best one.
In this paper, we propose a test for the null hypothesis that a decreasing density function belon... more In this paper, we propose a test for the null hypothesis that a decreasing density function belongs to a givenparametric family of distribution functions against the non-parametric alternative. This method, which is based on an empirical likelihood (EL) ratio statistic, is similar to the test introduced by Vexler and Gurevich [23]. The consistency of the test statistic proposed is derived under the null and alternative hypotheses. A simulation study is conducted to inspect the power of the proposed test under various decreasing alternatives. In each scenario, the critical region of the test is obtained using a Monte Carlo technique. The applicability of the proposed test in practice is demonstrated through a few real data examples.
Uploads
Papers by Vahid Fakoor