The aim of this expository paper is to present the properties of the linear skew-t distribution, which is a specific example of a symmetry modulated-distribution. The skewing function remains the distribution function of Student’s t, but its argument is simpler than that used for the standard skew-t. The linear skew-t offers different insights, for example, different moments and tail behavior, and can be simpler to use for empirical work. It is shown that the distribution may be expressed as a hidden truncation model. The paper describes an extended version of the distribution that is analogous to the extended skew-t. For certain parameter values, the distribution is bimodal. The paper presents expressions for the moments of the distribution and shows that numerical integration methods are required. A multivariate version of the distribution is described. The bivariate version of the distribution may also be bimodal. The distribution is not closed under marginalization, and stochastic ordering is not satisfied. The properties of the distribution are illustrated with numerous examples of the density functions, table of moments and critical values. The results in this paper suggest that the linear skew-t may be useful for some applications, but that it should be used with care for methodological work.
{"title":"The Linear Skew-t Distribution and Its Properties","authors":"C. Adcock","doi":"10.3390/stats6010024","DOIUrl":"https://doi.org/10.3390/stats6010024","url":null,"abstract":"The aim of this expository paper is to present the properties of the linear skew-t distribution, which is a specific example of a symmetry modulated-distribution. The skewing function remains the distribution function of Student’s t, but its argument is simpler than that used for the standard skew-t. The linear skew-t offers different insights, for example, different moments and tail behavior, and can be simpler to use for empirical work. It is shown that the distribution may be expressed as a hidden truncation model. The paper describes an extended version of the distribution that is analogous to the extended skew-t. For certain parameter values, the distribution is bimodal. The paper presents expressions for the moments of the distribution and shows that numerical integration methods are required. A multivariate version of the distribution is described. The bivariate version of the distribution may also be bimodal. The distribution is not closed under marginalization, and stochastic ordering is not satisfied. The properties of the distribution are illustrated with numerous examples of the density functions, table of moments and critical values. The results in this paper suggest that the linear skew-t may be useful for some applications, but that it should be used with care for methodological work.","PeriodicalId":93142,"journal":{"name":"Stats","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43915525","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The purpose of this note is to provide a description of the weak convergence of the random resample size bootstrap empirical process. The principal results are used to estimate the sample rank correlation coefficients using Spearman’s and Kendall’s respective methods. In addition to this, we discuss how our findings can be applied to statistical testing.
{"title":"On Weak Convergence of the Bootstrap Copula Empirical Process with Random Resample Size","authors":"S. Bouzebda","doi":"10.3390/stats6010023","DOIUrl":"https://doi.org/10.3390/stats6010023","url":null,"abstract":"The purpose of this note is to provide a description of the weak convergence of the random resample size bootstrap empirical process. The principal results are used to estimate the sample rank correlation coefficients using Spearman’s and Kendall’s respective methods. In addition to this, we discuss how our findings can be applied to statistical testing.","PeriodicalId":93142,"journal":{"name":"Stats","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46123298","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Researchers interested in the assessment of substance use trajectories, and predictors of change, have several data analysis options. These include, among others, generalized estimating equations and latent growth curve modeling. One difficulty in the assessment of substance use, however, is the nature of the variables studied. Although counting instances of use (e.g., the number of cigarettes smoked per day) would seem to be the best option, such data present difficulties in that the distribution of these variables is not likely normal. Count variables often follow a Poisson distribution, and when dealing with substance use in the general population, there is a preponderance of zeros (representing not using). As such, substance use counts may approximate a zero-inflated Poisson distribution. Unfortunately, analyses with zero-inflated Poisson random variables are not easily accommodated in many types of software and may be beyond access to most researchers. As such, an easier method would benefit researchers interested in assessing substance use change. The purpose of this study is to assess the area under the curve as an option when dealing with repeated measures data and contrast it to one popular method of longitudinal data analysis, latent growth curve modeling. Using a Monte Carlo simulation study with varying sample sizes, we found that the area under the curve performed well with different sample sizes and compared favorably to the performance of latent growth curve modeling, particularly when dealing with smaller sample sizes. The area under the curve may be a simpler alternative for researchers, especially when dealing with smaller sample sizes.
{"title":"Assessing Area under the Curve as an Alternative to Latent Growth Curve Modeling for Repeated Measures Zero-Inflated Poisson Data: A Simulation Study","authors":"Daniel Rodriguez","doi":"10.3390/stats6010022","DOIUrl":"https://doi.org/10.3390/stats6010022","url":null,"abstract":"Researchers interested in the assessment of substance use trajectories, and predictors of change, have several data analysis options. These include, among others, generalized estimating equations and latent growth curve modeling. One difficulty in the assessment of substance use, however, is the nature of the variables studied. Although counting instances of use (e.g., the number of cigarettes smoked per day) would seem to be the best option, such data present difficulties in that the distribution of these variables is not likely normal. Count variables often follow a Poisson distribution, and when dealing with substance use in the general population, there is a preponderance of zeros (representing not using). As such, substance use counts may approximate a zero-inflated Poisson distribution. Unfortunately, analyses with zero-inflated Poisson random variables are not easily accommodated in many types of software and may be beyond access to most researchers. As such, an easier method would benefit researchers interested in assessing substance use change. The purpose of this study is to assess the area under the curve as an option when dealing with repeated measures data and contrast it to one popular method of longitudinal data analysis, latent growth curve modeling. Using a Monte Carlo simulation study with varying sample sizes, we found that the area under the curve performed well with different sample sizes and compared favorably to the performance of latent growth curve modeling, particularly when dealing with smaller sample sizes. The area under the curve may be a simpler alternative for researchers, especially when dealing with smaller sample sizes.","PeriodicalId":93142,"journal":{"name":"Stats","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44589134","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This work presents a brief review on the modern approaches to data modeling by the methods developed in the quantum physics during the last one hundred years. Quantum computers and computations have already been widely investigated theoretically and attempted in some practical implementations, but methods of quantum data modeling are not yet sufficiently established. A vast range of concepts and methods of quantum mechanics have been tried in many fields of information and behavior sciences, including communications and artificial intelligence, cognition and decision making, sociology and psychology, biology and economics, financial and political studies. The application of quantum methods in areas other than physics is called the quantum-like paradigm, meaning that such approaches may not be related to the physical processes but rather correspond to data modeling by the methods designed for operating in conditions of uncertainty. This review aims to attract attention to the possibilities of these methods of data modeling that can enrich theoretical consideration and be useful for practical purposes in various sciences and applications.
{"title":"Quantum-like Data Modeling in Applied Sciences: Review","authors":"S. Lipovetsky","doi":"10.3390/stats6010021","DOIUrl":"https://doi.org/10.3390/stats6010021","url":null,"abstract":"This work presents a brief review on the modern approaches to data modeling by the methods developed in the quantum physics during the last one hundred years. Quantum computers and computations have already been widely investigated theoretically and attempted in some practical implementations, but methods of quantum data modeling are not yet sufficiently established. A vast range of concepts and methods of quantum mechanics have been tried in many fields of information and behavior sciences, including communications and artificial intelligence, cognition and decision making, sociology and psychology, biology and economics, financial and political studies. The application of quantum methods in areas other than physics is called the quantum-like paradigm, meaning that such approaches may not be related to the physical processes but rather correspond to data modeling by the methods designed for operating in conditions of uncertainty. This review aims to attract attention to the possibilities of these methods of data modeling that can enrich theoretical consideration and be useful for practical purposes in various sciences and applications.","PeriodicalId":93142,"journal":{"name":"Stats","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42785084","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
To what extent do high school students’ course grades align with their scores on standardized college admission tests? People sometimes make the argument that grades are “inflated”, but many school districts only use outcome-based descriptive methods for school evaluation. In order to answer that question, this paper proposes econometric models for panel data, which are less well-known in educational evaluation. In particular, fixed-effects and random-effects models are proposed for assessing student performance in university entrance examinations. School-level panel data analysis allows one knowing if results in college admission tests vary more between high schools than within a high school in different academic years. Another advantage of using panel data includes the ability to control for school-specific unobserved heterogeneity. For empirical implementation, official transcript data and university entrance test scores of Spanish secondary schools are used.
{"title":"Panel Data Models for School Evaluation: The Case of High Schools’ Results in University Entrance Examinations","authors":"Manuel Salas‐Velasco","doi":"10.3390/stats6010019","DOIUrl":"https://doi.org/10.3390/stats6010019","url":null,"abstract":"To what extent do high school students’ course grades align with their scores on standardized college admission tests? People sometimes make the argument that grades are “inflated”, but many school districts only use outcome-based descriptive methods for school evaluation. In order to answer that question, this paper proposes econometric models for panel data, which are less well-known in educational evaluation. In particular, fixed-effects and random-effects models are proposed for assessing student performance in university entrance examinations. School-level panel data analysis allows one knowing if results in college admission tests vary more between high schools than within a high school in different academic years. Another advantage of using panel data includes the ability to control for school-specific unobserved heterogeneity. For empirical implementation, official transcript data and university entrance test scores of Spanish secondary schools are used.","PeriodicalId":93142,"journal":{"name":"Stats","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43724277","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we develop a novel soft-clipping discrete beta GARCH (ScDBGARCH) model that provides an available method to model bounded time series with under-dispersion, equi-dispersion or over-dispersion. The new model not only allows positive dependence, but also negative dependence. The stochastic properties of the models are established, and these results are, in turn, used in the analysis of the asymptotic properties of the conditional maximum likelihood (CML) estimator of the new model. In addition, we apply the new model to measles infection to show its improved performance.
{"title":"A New Soft-Clipping Discrete Beta GARCH Model and Its Application on Measles Infection","authors":"Huaping Chen","doi":"10.3390/stats6010018","DOIUrl":"https://doi.org/10.3390/stats6010018","url":null,"abstract":"In this paper, we develop a novel soft-clipping discrete beta GARCH (ScDBGARCH) model that provides an available method to model bounded time series with under-dispersion, equi-dispersion or over-dispersion. The new model not only allows positive dependence, but also negative dependence. The stochastic properties of the models are established, and these results are, in turn, used in the analysis of the asymptotic properties of the conditional maximum likelihood (CML) estimator of the new model. In addition, we apply the new model to measles infection to show its improved performance.","PeriodicalId":93142,"journal":{"name":"Stats","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45415435","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this article, we establish a new class of nonparametric Shewhart-type control charts based on order statistics with signaling runs-type rules. The proposed charts offer to the practitioner the opportunity to reach, as close as possible, a pre-specified level of performance by determining appropriately their design parameters. Special monitoring schemes, already established in the literature, are ascertained to be members of the proposed class. In addition, several new nonparametric control charts that belong to the family are introduced and studied in some detail. Exact formulae for the variance of the run length distribution and the average run length (ARL) for the proposed monitoring schemes are also derived. A numerical investigation is carried out and demonstrates that the proposed schemes acquire competitive performance in detecting the shift of the underlying distribution. Although the large number of design parameters is quite hard to handle, the numerical results presented throughout the lines of the present manuscript provide practical guidance for the implementation of the proposed charts.
{"title":"A Class of Enhanced Nonparametric Control Schemes Based on Order Statistics and Runs","authors":"Nikolaos I. Panayiotou, I. Triantafyllou","doi":"10.3390/stats6010017","DOIUrl":"https://doi.org/10.3390/stats6010017","url":null,"abstract":"In this article, we establish a new class of nonparametric Shewhart-type control charts based on order statistics with signaling runs-type rules. The proposed charts offer to the practitioner the opportunity to reach, as close as possible, a pre-specified level of performance by determining appropriately their design parameters. Special monitoring schemes, already established in the literature, are ascertained to be members of the proposed class. In addition, several new nonparametric control charts that belong to the family are introduced and studied in some detail. Exact formulae for the variance of the run length distribution and the average run length (ARL) for the proposed monitoring schemes are also derived. A numerical investigation is carried out and demonstrates that the proposed schemes acquire competitive performance in detecting the shift of the underlying distribution. Although the large number of design parameters is quite hard to handle, the numerical results presented throughout the lines of the present manuscript provide practical guidance for the implementation of the proposed charts.","PeriodicalId":93142,"journal":{"name":"Stats","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41616162","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper proposes a heuristic reward reinforcement learning framework for point cloud registration. As an essential step of many 3D computer vision tasks such as object recognition and 3D reconstruction, point cloud registration has been well studied in the existing literature. This paper contributes to the literature by addressing the limitations of embedding and reward functions in existing methods. An improved state-embedding module and a stochastic reward function are proposed. While the embedding module enriches the captured characteristics of states, the newly designed reward function follows a time-dependent searching strategy, which allows aggressive attempts at the beginning and tends to be conservative in the end. We assess our method based on two public datasets (ModelNet40 and ScanObjectNN) and real-world data. The results confirm the strength of the new method in reducing errors in object rotation and translation, leading to more precise point cloud registration.
{"title":"Point Cloud Registration via Heuristic Reward Reinforcement Learning","authors":"Bingren Chen","doi":"10.3390/stats6010016","DOIUrl":"https://doi.org/10.3390/stats6010016","url":null,"abstract":"This paper proposes a heuristic reward reinforcement learning framework for point cloud registration. As an essential step of many 3D computer vision tasks such as object recognition and 3D reconstruction, point cloud registration has been well studied in the existing literature. This paper contributes to the literature by addressing the limitations of embedding and reward functions in existing methods. An improved state-embedding module and a stochastic reward function are proposed. While the embedding module enriches the captured characteristics of states, the newly designed reward function follows a time-dependent searching strategy, which allows aggressive attempts at the beginning and tends to be conservative in the end. We assess our method based on two public datasets (ModelNet40 and ScanObjectNN) and real-world data. The results confirm the strength of the new method in reducing errors in object rotation and translation, leading to more precise point cloud registration.","PeriodicalId":93142,"journal":{"name":"Stats","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49217426","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this research, we design the Farlie–Gumbel–Morgenstern bivariate moment exponential distribution, a bivariate analogue of the moment exponential distribution, using the Farlie–Gumbel–Morgenstern approach. With the analysis of real-life data, the competitiveness of the Farlie–Gumbel–Morgenstern bivariate moment exponential distribution in comparison with the other Farlie–Gumbel–Morgenstern distributions is discussed. Based on the Farlie–Gumbel–Morgenstern bivariate moment exponential distribution, we develop the distribution theory of concomitants of order statistics and derive the best linear unbiased estimator of the parameter associated with the variable of primary interest (study variable). Evaluations are also conducted regarding the efficiency comparison of the best linear unbiased estimator relative to the respective unbiased estimator. Additionally, empirical illustrations of the best linear unbiased estimator with respect to the unbiased estimator are performed.
{"title":"Farlie–Gumbel–Morgenstern Bivariate Moment Exponential Distribution and Its Inferences Based on Concomitants of Order Statistics","authors":"S. P. Arun, C. Chesneau, R. Maya, M. Irshad","doi":"10.3390/stats6010015","DOIUrl":"https://doi.org/10.3390/stats6010015","url":null,"abstract":"In this research, we design the Farlie–Gumbel–Morgenstern bivariate moment exponential distribution, a bivariate analogue of the moment exponential distribution, using the Farlie–Gumbel–Morgenstern approach. With the analysis of real-life data, the competitiveness of the Farlie–Gumbel–Morgenstern bivariate moment exponential distribution in comparison with the other Farlie–Gumbel–Morgenstern distributions is discussed. Based on the Farlie–Gumbel–Morgenstern bivariate moment exponential distribution, we develop the distribution theory of concomitants of order statistics and derive the best linear unbiased estimator of the parameter associated with the variable of primary interest (study variable). Evaluations are also conducted regarding the efficiency comparison of the best linear unbiased estimator relative to the respective unbiased estimator. Additionally, empirical illustrations of the best linear unbiased estimator with respect to the unbiased estimator are performed.","PeriodicalId":93142,"journal":{"name":"Stats","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46566410","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this article, we introduce two new bivariate Kumaraswamy (KW)-type distributions with univariate Kumaraswamy marginals (under certain parametric restrictions) that are less restrictive in nature compared with several other existing bivariate beta and beta-type distributions. Mathematical expressions for the joint and marginal density functions are presented, and properties such as the marginal and conditional distributions, product moments and conditional moments are obtained. Additionally, we show that both the proposed bivariate probability models have positive likelihood ratios dependent on a potential model for fitting positively dependent data in the bivariate domain. The method of maximum likelihood and the method of moments are used to derive the associated estimation procedure. An acceptance and rejection sampling plan to draw random samples from one of the proposed models along with a simulation study are also provided. For illustrative purposes, two real data sets are reanalyzed from different domains to exhibit the applicability of the proposed models in comparison with several other bivariate probability distributions, which are defined on [0,1]×[0,1].
{"title":"A New Class of Alternative Bivariate Kumaraswamy-Type Models: Properties and Applications","authors":"I. Ghosh","doi":"10.3390/stats6010014","DOIUrl":"https://doi.org/10.3390/stats6010014","url":null,"abstract":"In this article, we introduce two new bivariate Kumaraswamy (KW)-type distributions with univariate Kumaraswamy marginals (under certain parametric restrictions) that are less restrictive in nature compared with several other existing bivariate beta and beta-type distributions. Mathematical expressions for the joint and marginal density functions are presented, and properties such as the marginal and conditional distributions, product moments and conditional moments are obtained. Additionally, we show that both the proposed bivariate probability models have positive likelihood ratios dependent on a potential model for fitting positively dependent data in the bivariate domain. The method of maximum likelihood and the method of moments are used to derive the associated estimation procedure. An acceptance and rejection sampling plan to draw random samples from one of the proposed models along with a simulation study are also provided. For illustrative purposes, two real data sets are reanalyzed from different domains to exhibit the applicability of the proposed models in comparison with several other bivariate probability distributions, which are defined on [0,1]×[0,1].","PeriodicalId":93142,"journal":{"name":"Stats","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45919586","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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