Model checks for two-sample location-scale

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY Journal of Nonparametric Statistics Pub Date : 2023-08-04 DOI:10.1080/10485252.2023.2243350

Atefeh Javidialsaadi, Shoubhik Mondal, Sundarraman Subramanian

{"title":"Model checks for two-sample location-scale","authors":"Atefeh Javidialsaadi, Shoubhik Mondal, Sundarraman Subramanian","doi":"10.1080/10485252.2023.2243350","DOIUrl":null,"url":null,"abstract":"MODEL CHECKS FOR TWO-SAMPLE LOCATION-SCALE by Atefeh Javidialsaadi Two-sample location-scale refers to a model that permits a pair of standardized random variables to have a common distribution. This means that if X1 and X2 are two random variables with means μ1 and μ2 and standard deviations σ1 and σ2, then (X1−μ1)/σ1 and (X2−μ2)/σ2 have some common unspecified standard or base distribution F0. Function-based hypothesis testing for these models refers to formal tests that would help determine whether or not two samples may have come from some location-scale family of distributions, without specifying the standard distribution F0. For uncensored data, Hall et al. (2013) proposed a test based on empirical characteristic functions (ECFs), but it can not be directly applied for censored data. Empirical likelihood with minimum distance (MD) plug-ins provides an alternative to the approach based on ECFs (Subramanian, 2020). However, when working with standardized data, it appeared feasible to set up plug-in empirical likelihood (PEL) with estimated means and standard deviations as plug-ins, which avoids MD estimation of location and scale parameters and (hence) quantile estimation. This project addresses two issues: (i) Set up a PEL founded testing procedure that uses sample means and standard deviations as the plug-ins for uncensored case, and Kaplan–Meier integral based estimators as plug-ins for censored case, (ii) Extend the ECF test to accommodate censoring. Large sample null distributions of the proposed test statistics are derived. Numerical studies are carried out to investigate the performance of the proposed methods. Real examples are also presented for both the uncensored and censored cases. MODEL CHECKS FOR TWO-SAMPLE LOCATION-SCALE by Atefeh Javidialsaadi A Dissertation Submitted to the Faculty of New Jersey Institute of Technology and Rutgers, The State University of New Jersey – Newark in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Mathematical Sciences Department of Mathematical Sciences Department of Mathematics and Computer Science, Rutgers-Newark","PeriodicalId":50112,"journal":{"name":"Journal of Nonparametric Statistics","volume":"33 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2023-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Nonparametric Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/10485252.2023.2243350","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}

引用次数: 0

Abstract

MODEL CHECKS FOR TWO-SAMPLE LOCATION-SCALE by Atefeh Javidialsaadi Two-sample location-scale refers to a model that permits a pair of standardized random variables to have a common distribution. This means that if X1 and X2 are two random variables with means μ1 and μ2 and standard deviations σ1 and σ2, then (X1−μ1)/σ1 and (X2−μ2)/σ2 have some common unspecified standard or base distribution F0. Function-based hypothesis testing for these models refers to formal tests that would help determine whether or not two samples may have come from some location-scale family of distributions, without specifying the standard distribution F0. For uncensored data, Hall et al. (2013) proposed a test based on empirical characteristic functions (ECFs), but it can not be directly applied for censored data. Empirical likelihood with minimum distance (MD) plug-ins provides an alternative to the approach based on ECFs (Subramanian, 2020). However, when working with standardized data, it appeared feasible to set up plug-in empirical likelihood (PEL) with estimated means and standard deviations as plug-ins, which avoids MD estimation of location and scale parameters and (hence) quantile estimation. This project addresses two issues: (i) Set up a PEL founded testing procedure that uses sample means and standard deviations as the plug-ins for uncensored case, and Kaplan–Meier integral based estimators as plug-ins for censored case, (ii) Extend the ECF test to accommodate censoring. Large sample null distributions of the proposed test statistics are derived. Numerical studies are carried out to investigate the performance of the proposed methods. Real examples are also presented for both the uncensored and censored cases. MODEL CHECKS FOR TWO-SAMPLE LOCATION-SCALE by Atefeh Javidialsaadi A Dissertation Submitted to the Faculty of New Jersey Institute of Technology and Rutgers, The State University of New Jersey – Newark in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Mathematical Sciences Department of Mathematical Sciences Department of Mathematics and Computer Science, Rutgers-Newark

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

两样本位置尺度的模型检验

双样本位置尺度是指允许一对标准化随机变量具有共同分布的模型。这意味着，如果X1和X2是均值为μ1和μ2，标准差为σ1和σ2的两个随机变量，则(X1−μ1)/σ1和(X2−μ2)/σ2具有某种共同的未指定的标准或基本分布F0。这些模型的基于函数的假设检验是指在不指定标准分布F0的情况下，帮助确定两个样本是否可能来自某个位置尺度分布家族的正式检验。对于未经删减的数据，Hall等(2013)提出了一种基于经验特征函数(ECFs)的检验方法，但不能直接应用于删减数据。最小距离(MD)插件的经验似然提供了一种基于ecf的替代方法(Subramanian, 2020)。然而，当处理标准化数据时，将估计的平均值和标准差设置为插件的插件经验似然(PEL)似乎是可行的，这避免了位置和尺度参数的MD估计以及(因此)分位数估计。该项目解决了两个问题:(i)建立一个PEL创建的测试程序，该程序使用样本均值和标准差作为未审查情况的插件，并使用基于Kaplan-Meier积分的估计器作为审查情况的插件，(ii)扩展ECF测试以适应审查。提出了检验统计量的大样本零分布。数值研究了所提出的方法的性能。并对未删节和删节两种情况给出了实例。提交给新泽西州立大学纽瓦克分校新泽西理工学院和罗格斯学院的论文，部分满足数学科学系数学与计算机科学系哲学博士学位的要求

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文去求助

来源期刊

Journal of Nonparametric Statistics 数学-统计学与概率论

CiteScore

1.50

自引率

8.30%

发文量

审稿时长

6-12 weeks

期刊介绍： Journal of Nonparametric Statistics provides a medium for the publication of research and survey work in nonparametric statistics and related areas. The scope includes, but is not limited to the following topics: Nonparametric modeling, Nonparametric function estimation, Rank and other robust and distribution-free procedures, Resampling methods, Lack-of-fit testing, Multivariate analysis, Inference with high-dimensional data, Dimension reduction and variable selection, Methods for errors in variables, missing, censored, and other incomplete data structures, Inference of stochastic processes, Sample surveys, Time series analysis, Longitudinal and functional data analysis, Nonparametric Bayes methods and decision procedures, Semiparametric models and procedures, Statistical methods for imaging and tomography, Statistical inverse problems, Financial statistics and econometrics, Bioinformatics and comparative genomics, Statistical algorithms and machine learning. Both the theory and applications of nonparametric statistics are covered in the journal. Research applying nonparametric methods to medicine, engineering, technology, science and humanities is welcomed, provided the novelty and quality level are of the highest order. Authors are encouraged to submit supplementary technical arguments, computer code, data analysed in the paper or any additional information for online publication along with the published paper.