Non-parametric methods

This Chapter is about the techniques, formal and informal, that are commonly used to give quantitative answers in the field of distributional analysis-covering subjects including inequality, poverty and the modelling of income distributions. It deals with parametric and non-parametric approaches and the way in which imperfections in data may be handled in practice

https://towardsdatascience.com/data-smoothing-for-data-science-visualization-the-goldilocks-trio-part-1-867765050615

Making peace with piecewise. We've all heard that information is beautiful. But then life happens, and we find ourselves trying to prettify the mess that often is reality…

Non-parametric option pricing models, such as artificial neural networks, are often found to outperform their parametric counterparts in empirical option pricing exercises. In this context, non-parametric models are viewed as more flexible and amenable to adaptive learning. However, the main drawback of non-parametric approaches is their lack of stability, which is detrimental to out-of-sample performance. This is the key reason why one may prefer a parsimonious parametric model. This paper proposes a parametric Takagi-Sugeno-Kang (TSK) fuzzy rule-based option pricing model that requires only a small number of rules to describe highly complex non-linear functions. The findings for this data-driven approach indicate that the TSK model presents a robust option pricing tool that is superior to an array of well-known parametric models from the literature. In addition, its predictive performance is consistently no worse than that of a non-parametric feedforward neural network model.

Statistika pada dasarnya dapat dibagi atas Statistika Deskriptif dan Statistika Inferensial/Induktif. Statistika Deskriptif meliputi prosedur, proses dan tahapan dalam peringkasan hasil-hasil pengamatan secara kuantitatif. Dalam pengertian lain statistika deskriptif mempelajari cara-cara pengumpulan, penyusunan, dan penyajian data suatu penelitian. Tujuan utama dari statistika deskriptif adalah membantu menggambarkan fakta sehingga lebih mudah dibaca dan dipahami.
Statistika induktif adalah statistika yang terkait dengan penarikan kesimpulan serta pengambilan keputusan berdasarkan fakta. Dalam pengertian lain, statistika induktif juga didefinisikan sebagai statistika yang mempelajari cara-cara penarikan suatu kesimpulan dari suatu populasi tertentu berdasarkan sebagian data (sampel). Dalam penarikan kesimpulan tersebut, statistik induktif mengacu kepada suatu pengujian hipotesis tertentu.
Selanjutnya, dalam statistika induktif, berbagai prosedur dan uji statistik yang dapat digunakan pada dasarnya dapat dikelompokkan menjadi dua kelompok, yakni kelompok Statistik Parametrik dan kelompok Statistik Non-Parametrik. Uji Statistik Parametrik ialah suatu uji yang modelnya menetapkan adanya syarat-syarat tertentu (asumsi-asumsi) dari sebaran (distribusi) data populasinya. Statistika parametik lebih banyak digunakan untuk menganalisis data yang berskala interval dan rasio dengan dilandasi asumsi tertentu seperti normalitas. Oleh karenanya, makna hasil suatu uji parametrik tergantung pada validitas asumsi-asumsi tersebut. Selain itu, jika dilihat dari jumlah datanya, biasanya data berjumlah besar, sekurang-kurangnya lebih besar atau sama dengan 30 data.

This paper is intended to elucidate some implications of usage-based linguistic theory for statistical and computational models of language acquisition, focusing on morphology and morphophonology. I discuss the need for grammar (a.k.a. abstraction), the contents of individual grammars (a potentially infinite number of constructions, paradigmatic mappings and predictive relationships between phonological units), the computational characteristics of constructions (complex non-crossover interactions among partially redundant features), resolution of competition among constructions (probability matching), and the need for multimodel inference in modeling internal grammars underlying the linguistic performance of a community.

Se hace  una sucinta presentación del desarrollo de las tablas de contingencia,  así como  los elementos básicos de las tablas de contingencia discutiendo algunos detalles que, al no considerarlos invalidan, las generalizaciones que se hacen usando los métodos que comúnmente se introducen en los cursos de estadística.  Se presentan los elementos básicos de las  medidas de asociación y se analizan algunos coeficientes que caracterizan las propiedades de las relaciones que aparecen entre las variables.

KEYWORDS: Tablas de contingencia, medidas de asociación, pruebas

"Considerable intellectual progress has been made to the development of various semiparametric varying-coefficient models over the past ten to fifteen years. An important advantage of these models is that they avoid much of the curse of dimensionality problem as the nonparametric functions are restricted only to some variables.  More recently, varying-coefficient methods have been applied to quantile regression modeling, but all previous studies assume that the data are fully observed.  The purpose of this paper is two-fold. We first develop a varying-coefficient approach to the estimation of regression quantiles under random data censoring.  We use a weighted inverse probability approach to account for censoring, and propose a majorize-minimize type algorithm to solve the non-smooth weighted estimating equations.  The asymptotic properties of the proposed estimator of the nonparametric functions are studied, and a resampling method is developed for obtaining the estimator of the sampling variance.  An important aspect of our method is that it allows the censoring time to depend on the covariates.  Second, we show that this varying-coefficient procedure can be further improved when implemented within a composite quantile regression framework.  Composite quantile regression has recently gained considerable attention due to its ability to combine information across different quantile functions.  We assess the finite sample properties of the proposed procedures in simulated studies.  Real data applications are also considered.
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Our dataset is based on a larger dataset containing the results for 200 volunteers and 900 microorganisms. From this dataset 40 individuals were randomly selected. 8 microorganisms were also selected. Their relative abundances were corrected so that their total was 100%. The fact that the original dataset is based on self-selection, makes it doubtful that the selection of the individuals is 'truly random'. We will however assume that they are. 13 individuals are obese, 27 are non-obese. There are no missing values for BMI. 15 individuals are female, 24 male. For one individual the gender is not known. 7 men and 6 women are obese. 8 men are non-obese and the same is true for 18 women.

This paper investigates an approach to the use of fractals in architectural design. Two major aspects are discussed. First, the effect of the direction of the line segments on the generated fractal, as well as, the proportions between the generator and the initiator. Secondly, the meanings attached to the lines segments that constitute the fractal are based on some known architectural organization. The goal is to develop a basis for using fractals to suggest architectural forms.

"There have been a lot of issues regarding the efficiency of Public Sector banks. The private sector banks are generally said to utilize resources in a more efficient manner. The study deals with the comparison of the efficiency levels of private and public sector banks. Among the public sector banks 18 public sector banks have been taken in to account apart from the State Bank of India (SBI) group.  Data envelopment analysis has been used as tool for measuring the efficiency level of each sector. The interest and expenditure costs have been taken as the inputs while the advances have been taken as the output. The non parametric method of data envelopment analysis has widely been used in the field of judging efficiency of banks. In this study too we use the concept of Data Envelopment Analysis to judge the efficiency level of each bank or decision making unit. The efficiency in the study is the cost efficiency. The input taken into account consists of the operating expense and interest expense while the output consists of total amount of loans and advances. The time frame that has been taken is the post recession period from 2009 to 2011.
Keywords: public sector banks, private sector banks, cost efficiency, data envelopment analysis.
"

El presente artículo presenta la metodología para
analizar las expectativas y percepciones del cliente en tres
tipos de empresas de servicio distintas utilizando el cuestionario SERVQUAL propuesto por Parasuraman, la metodología hace hincapié en el uso de pruebas no paramétricas, concretamente tablas de contingencia y pruebas de Chi-cuadrada para verificar su dependencia o independencia y, de esta manera, determinar el futuro plan de mejora de cada dimensión en particular. Se muestra además un caso que no cumple con la condición de uso de la prueba Chi-cuadrada y su posterior tratamiento.

GmAMisc is a R package that collects a number of functions that I have built in different points in time. The functions' aim spans from univariate outlier detection, to permutation t test, permutation chi-square test, calculation of Brainerd-Robinson similarity coefficient, validation of logistic regression models, calculation of Posterior Probability for the chronological relations between two Bayesian radiocarbon phases, and more. The package comes with some toy datasets.

This paper has two contributions to the International Financial Reporting Stands (IFRS) adoption literature. First is the scrutinizing impact of IFRS adoption on value relevance in the UK with TEST-A analysis under the H 01 hypothesis. The second contribution is capturing the impact of IFRS adoption on key financial indicators of firms with the TEST-B analysis that hypothesizes H 02 .The statistical differences of items of two different reporting standards are examined with non-parametric tests as all input variables failed the Shapiro-Wilk and Lilliefors normality tests in TEST-A. The finding rejects the H 01 hypothesis for BvMv, and agrees that IFRS has impact on value relevance. Besides, Ohlson's (1995) model documents that the coefficient of dummy variable (MODE) is positive. Therefore, the analysis concludes that IFRS has positive impact on value relevance. The aftermath of TEST-B rejects the H 02 hypothesis for all profitability ratios (ROE, ROCE, ROA, PM) and gearing ratios (GR). It concludes that profitability and gearing ratios are affected by IFRS adoption, whereas efficiency-liquidity ratios are not. Also, in Forward Stepwise regression analysis only ROCE, ROA, and PM ratios show significant results. The analysis documents positive and significant impact of IFRS on these three ratios.

Doukhan and Louhichi introduced a covariance-based concept of weak dependence which is more general than classical mixing concepts. We prove a Bernstein-type inequality under this condition which is similar to the well-known inequality in the independent case. We apply this tool to derive asymptotic properties of penalized least-squares estimators in Barron's classes.

Non-parametric kernel methods are becoming more commonplace for data analysis, modeling, and inference. Unfortunately, these methods are known to be computationally burdensome. The burden increases as the amount of available data rises and can quickly overwhelm the computational resources present in modern desktop workstations. Approximation-based approaches exist which can dramatically reduce execution time, however, these approaches remain just thatapproximations, however good they may be. Along with the approximate nature of such approaches, they do not admit multivariate kernel estimation with general bandwidths (ÿxed, variable, and adaptive). In this paper, I consider a parallel implementation of a number of popular kernel methods based on the MPI standard. MPI is a freely available parallel distributed library that runs on 'commodity hardware' such as a network of workstations typically found in many o ce environments. A simple demonstration indicates how one can dramatically reduce the computational burden often associated with kernel methods thereby achieving an almost 'ideal' parallel speed-up, while the approach is valid for multivariate kernel estimation with general bandwidths and does not rely on approximations. Some straightforward applications illustrate just how disarmingly simple the MPI library can be to use.

Modal regression estimates the local modes of the distribution of Y given X = x, instead of the mean, as in the usual regression sense, and can hence reveal important structure missed by usual regression methods. We study a simple nonparametric method for modal regression, based on a kernel density estimate (KDE) of the joint distribution of Y and X. We derive asymptotic error bounds for this method, and propose techniques for constructing confidence sets and prediction sets. The latter is used to select the smoothing bandwidth of the underlying KDE. The idea behind modal regression is connected to many others, such as mixture regression and density ridge estimation, and we discuss these ties as well.

Financial markets are often found to exhibit uncanny behavior despite being recognized as highly efficient.  One well documented behavior pertains to the day-of-the-week effect.  Earlier studies reveal significant negative returns of Mondays, prompting some researchers to call the phenomenon "Monday" or "Weekend" effect. This occurrence, supports the existence of  inefficient markets which can provide investors and speculators opportunities for arbitrage.  This anomaly poses a distinct challenge to the Efficient Market Hypothesis (EMH) as applied to the behavior of stock prices in the Philippine Stock Exchange (PSE), particularly in a period spanning the ongoing modernization when the PSE started embarking on state-of-the-art systems improvement aimed at enhancing information disclosure and  integrity of  market transactions. Three non-parametric procedures are utilized to test the existence of the day-of-the-week effect using contemporary data via a one-way classification experimental lay-out applied on the overall PSE index and on the indices of all of its six subsectoral markets.  These procedures include the Kruskall-Wallis, Steel-Dwass-Critchlow-Fligner Multiple Comparison Procedures and the Bonferonni Correction approach.  These techniques employ cutting-edge non-parametric statistical procedures that include a level of significance correction to obviate the possibility of “false positive” outcomes in the pair-wise multiple comparison tests of trading day effects.  Results reveal the non-existence of the day-of-the-week effects on the main index, as well as on the sub-sectoral indices.  The findings further support the empirical validity of the EMH, lending credence to the efficacy of the modernization program. Hence, the potential challenge to the weak form market efficiency of the local stock market posed by day-of-the-week effect does not exist during the modern contemporary period

Financial markets are often found to exhibit uncanny behavior despite being recognized as highly efficient. One well documented behavior pertains to the day-of-the-week effect. Earlier studies reveal significant negative returns of Mondays, prompting some researchers to call the phenomenon "Monday" or "Weekend" effect. This occurrence, supports the existence of inefficient markets which can provide investors and speculators opportunities for arbitrage. This anomaly poses a distinct challenge to the Efficient Market Hypothesis (EMH) as applied to the behavior of stock prices in the Philippine Stock Exchange (PSE), particularly in a period spanning the ongoing modernization when the PSE started embarking on state-of-the-art systems improvement aimed at enhancing information disclosure and integrity of market transactions. Three non-parametric procedures are utilized to test the existence of the day-of-the-week effect using contemporary data via a one-way classifica...

Image recognition tasks use different approaches when it is necessary to restore the distribution function of a continuous random quantity under the condition of limiting the law of distribution. Similar situations occur when the image is noisy and there is a small sample of observations. The article discusses non-parametric methods of restoring the distribution function in recognition tasks.

Neste trabalho introduzimos a curvatura do perfil de brilho de uma galáxia, como uma maneira não paramétrica para identificar suas componentes estruturais. Tais componentes como por exemplo, bojos, barras, discos, braços espirais, lentes, anéis, entre outras, são fundamentais para o entendimento do caminho formativo e evolutivo em que as galáxias se submeteram. Identificá-las é também crucial para a classificação morfológica de galáxias. Com essa nova medida, foram analisadas em detalhe a curvatura de 16 galáxias com variadas morfologias. Uma alta (baixa) taxa de variação do perfil de brilho mostra altos (baixos) valores absolutos de curvatura. Além disso, regiões de transição entre componentes mostram altos valores de curvatura. Com essa nova metodologia foram identificados padrões que caracterizam bojo (pseudo ou clássico), discos, barras e anéis. O procedimento de cálculo e análise poderá ser automatizado em breve para lidar com o processamento de uma grande quantidade de dados e identificar as componentes das respectivas galáxias de uma forma automática, ou fornecer um ponto inicial para tal análise onde se utilizam métodos tradicionais de modelagem da distribuição de luz de múltiplas componentes. Como complemento, ao que nos motivou a introdução da medida de curvatura, analisamos como é o comportamento de ajustes de Sérsic únicos (e.g. n) e do índice de concentração C para galáxias de múltiplas componentes. Foram obtido que tais galáxias possuem altos valores dessas medidas (C e n) e são comparáveis aos medidos em galáxias de componentes únicas, portanto levando a classificação errônea dessas galáxias.

In fMRI research, the goal of correcting for multiple comparisons is to identify areas of activity that reflect true effects, and thus would be expected to replicate in future studies. Finding an appropriate balance between trying to minimize false positives (Type I error) while not being too stringent and omitting true effects (Type II error) can be challenging. Furthermore, the advantages and disadvantages of these types of errors may differ for different areas of study. In many areas of social neuroscience that involve complex processes and considerable individual differences, such as the study of moral judgment, effects are typically smaller and statistical power weaker, leading to the suggestion that less stringent corrections that allow for more sensitivity may be beneficial, but also result in more false positives. Using moral judgment fMRI data, we evaluated four commonly used methods for multiple comparison correction implemented in SPM12 by examining which method produced the most precise overlap with results from a meta-analysis of relevant studies and with results from nonparametric permutation analyses. We found that voxel-wise thresholding with family-wise error correction based on Random Field Theory provides a more precise overlap (i.e., without omitting too few regions or encompassing too many additional regions) than either clusterwise thresholding, Bonferroni correction, or false discovery rate correction methods.

The present study aims at the analysis of data obtained from patients with Uterine Fibroid. The studies consist of data obtained from 105 patients in respect of clinical and follow up actions for the treatment of Fibroid. Non-parametric methods viz., Kaplan-Meier, Product-limit method, Log Rank Test and Cox Regression models have been used for analyzing the Fibroid data. The analysis revealed the significant role played by certain variables in the survival of patients with Fibroids.

The aim of this work is to identify the existence of spatial spillover and spatial heterogeneity in local government efficiency, by using data from a newly constructed database about 341 municipalities from the Italian region Emilia-Romagna. The methodology is based on a two-step procedure. In the first step, cost efficiency scores are estimated by means of non-parametric Data Envelopment Analysis (DEA). In the second step, an Exploratory Spatial Data Analysis (ESDA), which is based on Moran’s I statistic, is applied to the efficiency scores computed in the previous step. Results show that municipalities are cost inefficient, on average, and that positive spatial externalities, in the form of positive spatial autocorrelation, influence the efficiency performance of local government. In particular, municipalities with a high degree of cost efficiency are surrounded by municipalities with a similar level of efficiency and vice versa. At the same time, results also show the existence of relevant spatial heterogeneity. Particular attention has been paid to the heterogeneity coming from outlying observations. Spatial spillovers provide evidence favoring theories of yardstick competition or phenomena like monitoring, benchmarking and knowledge transfer across space. At the same time, the presence of relevant spatial heterogeneity should be further investigated.

"This paper develops a nonparametric varying-coefficient approach for modeling the expectile-based Value at Risk (EVaR).  EVaR has an advantage over the conventional quantile-based VaR (QVaR) in being more sensitive than the latter to the magnitude of extreme losses.  EVaR can also be used for calculating QVaR and Expected Shortfall (ES) by exploiting the one-to-one mapping from expectiles to quantiles, and the relationship between VaR and ES.  Previous studies on conditional EVaR estimation only considered parametric autoregressive model set-ups, which account for the stochastic dynamics of asset returns but ignore other exogenous economic and investment related factors. Our approach overcomes this drawback and allows expectiles to be modeled directly using covariates that may be exogenous or lagged dependent in a flexible way. Risk factors associated with profits and losses can then be identified via the expectile regression at different levels of prudentiality.
We develop a local linear smoothing technique for estimating the coefficient functions within an asymmetric least squares minimization setting, and establish the consistency and asymptotic normality of the resultant estimator.  To save computing time, we propose the use of a one-step weighted local least squares procedure in computing the estimates.  Our simulation results show that the computing advantage afforded by this one-step procedure over full iteration is not compromised by a deterioration in estimation accuracy.  Real data examples are used to illustrate our method."

Many real-world applications call for learning predictive relationships from multi-modal data. In particular, in multi-media and web applications, given a dataset of images and their associated captions, one might want to construct a predictive model that not only predicts a caption for the image but also labels the individual objects in the image. We address this problem using a multi-modal hierarchical Dirichlet Process model (MoM-HDP) -a stochastic process for modeling multimodal data. MoM-HDP is an analog of a multi-modal Latent Dirichlet Allocation (MoM-LDA) with an infinite number of mixture components. Thus MoM-HDP allows circumventing the need for a priori choice of the number of mixture components or the computational expense of model selection. During training, the model has access to an un-segmented image and its caption, but not the labels for each object in the image. The trained model is used to predict the label for each region of interest in a segmented image. The model parameters are estimated efficiently using variational inference. We use two large benchmark datasets to compare the performance of the proposed MoM-HDP model with that of MoM-LDA model as well as some simple alternatives: Naive Bayes and Logistic Regression classifiers based on the formulation of the image annotation and imagelabel correspondence problems as one-against-all classification. Our experimental results show that unlike MoM-LDA, the performance of MoM-HDP is invariant to the number of mixture components. Furthermore, our experimental evaluation shows that the generalization performance of MoM-HDP is superior to that of MoM-HDP as well as the one-against-all Naive Bayes and Logistic Regression classifiers.

Amplification of genomic sequences flanked by delta elements of retrotransposons TY1 and TY2 is a reliable method for characterization of Saccharomyces cerevisiae strains. The aim of this study is to evaluate the usefulness of microfluidic electrophoresis (Caliper LabChip ®) to assess the factors that affect interlaboratory reproducibility of interdelta sequence typing for S. cerevisiae strain delimitation. We carried out experiments in two laboratories, using varying combinations of Taq DNA polymerases and thermal cyclers. The reproducibility of the technique is evaluated using nonparametric statistical tests and we show that the source of Taq DNA polymerase and technical differences between laboratories have the highest impact on reproducibility, whereas thermal cyclers have little impact. We also show that the comparative analysis of interdelta patterns is more reliable when fragment sizes are compared, than when absolute and relative DNA concentrations of each band are considered. Interdelta analysis based on a smaller fraction of bands with intermediate sizes between 100 and 1000 bp yield the highest reproducibility.

This research paper presents statistical comparisons between two methods that are commonly used to estimate option implied Risk-Neutral Densities (RND). These are: 1) mixture of lognormals (MXL); and, 2) volatility function technique (VFT). The former is a parametric method whilst the latter is a non-parametric approach. The RNDs are extracted from over-thecounter European-style options on the Mexican Peso–US Dollar exchange rate. The non-parametric method was the superior one for out-of-sample evaluations. The implied mean, median and mode were, in general, statistically different between the competing approaches. It is recommended to apply the VFT instead of the MXL given that the former has superior accuracy and it can be estimated when there is a relatively short crosssection of option exercise price range. The results have implications for financial investors and policy makers given that they could use the information content in options to analyze market’s perceptions about the...

Cost estimation of new products has always been difficult as only few design, manufacturing and operational features will be known. In these situations, parametric or non-parametric methods are commonly used to estimate the cost of a product given the corresponding cost drivers. The parametric models use priori determined cost function where the parameters of the function are evaluated from historical data. Non-parametric methods, on the other hand, attempt to fit curves to the historic data without predetermined function. In both methods, it is assumed that the historic data used in the analysis is a true representation of the relation between the cost drivers and the corresponding costs. However, because of efficiency variations of the manufacturers and suppliers, changes in supplier selections, market fluctuations, and several other reasons, certain costs in the historic data may be too high whereas other costs may represent better deals for their corresponding cost drivers. Thus, it may be important to rank the historic data and identify benchmarks and estimate the target costs of the product based on these benchmarks. In this paper, a novel adaptation of cost drivers and cost data is introduced in order to use data envelopment analysis for the purpose of ranking cost data and identify benchmarks, and then estimate the target costs of a new product based on these benchmarks. An illustrative case study has been presented for the cost estimation of landing gears of an aircraft manufactured by an aerospace company located in Montreal, CANADA.