{"title":"结合相关随机变量的回归分析的异方差诊断","authors":"A. Sheikhi, Fereshteh Arad, R. Mesiar","doi":"10.1214/22-bjps532","DOIUrl":null,"url":null,"abstract":"One of the most important assumptions in multiple regression analysis is the independence of the explanatory variables, however, this assumption is violated in several situations. In this work, we investigate regression equations when this independence does not hold and the explanatory variables are connected by many of elliptical copulas. We apply the proposed regression equation to study its heteroscedasticity diagnostic and using simulated data we also assess our regression model. A cross-validation procedure is carried out to ensure the unbiasedness of the results. Also, a real data analysis is presented as an application.","PeriodicalId":51242,"journal":{"name":"Brazilian Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A heteroscedasticity diagnostic of a regression analysis with copula dependent random variables\",\"authors\":\"A. Sheikhi, Fereshteh Arad, R. Mesiar\",\"doi\":\"10.1214/22-bjps532\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"One of the most important assumptions in multiple regression analysis is the independence of the explanatory variables, however, this assumption is violated in several situations. In this work, we investigate regression equations when this independence does not hold and the explanatory variables are connected by many of elliptical copulas. We apply the proposed regression equation to study its heteroscedasticity diagnostic and using simulated data we also assess our regression model. A cross-validation procedure is carried out to ensure the unbiasedness of the results. Also, a real data analysis is presented as an application.\",\"PeriodicalId\":51242,\"journal\":{\"name\":\"Brazilian Journal of Probability and Statistics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2022-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Brazilian Journal of Probability and Statistics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1214/22-bjps532\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Brazilian Journal of Probability and Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1214/22-bjps532","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
A heteroscedasticity diagnostic of a regression analysis with copula dependent random variables
One of the most important assumptions in multiple regression analysis is the independence of the explanatory variables, however, this assumption is violated in several situations. In this work, we investigate regression equations when this independence does not hold and the explanatory variables are connected by many of elliptical copulas. We apply the proposed regression equation to study its heteroscedasticity diagnostic and using simulated data we also assess our regression model. A cross-validation procedure is carried out to ensure the unbiasedness of the results. Also, a real data analysis is presented as an application.
期刊介绍:
The Brazilian Journal of Probability and Statistics aims to publish high quality research papers in applied probability, applied statistics, computational statistics, mathematical statistics, probability theory and stochastic processes.
More specifically, the following types of contributions will be considered:
(i) Original articles dealing with methodological developments, comparison of competing techniques or their computational aspects.
(ii) Original articles developing theoretical results.
(iii) Articles that contain novel applications of existing methodologies to practical problems. For these papers the focus is in the importance and originality of the applied problem, as well as, applications of the best available methodologies to solve it.
(iv) Survey articles containing a thorough coverage of topics of broad interest to probability and statistics. The journal will occasionally publish book reviews, invited papers and essays on the teaching of statistics.