当协变量和误差相关时非线性回归模型的带符号秩估计

IF 0.6 4区数学 Q3 STATISTICS & PROBABILITY

Annals of the Institute of Statistical Mathematics Pub Date : 2025-04-30 DOI:10.1007/s10463-025-00929-w

Hira L. Koul, Palaniappan Vellaisamy

{"title":"当协变量和误差相关时非线性回归模型的带符号秩估计","authors":"Hira L. Koul, Palaniappan Vellaisamy","doi":"10.1007/s10463-025-00929-w","DOIUrl":null,"url":null,"abstract":"<div><p>This paper contains the proof of the asymptotic uniform linearity of a sequence of simple linear signed-rank statistics based on the residuals of a class of nonlinear parametric regression models, where regression errors are possibly dependent on the covariates. This result in turn is used to prove the asymptotic normality of a signed rank estimator of the regression parameter vector in the given nonlinear regression model where covariates and regression errors are dependent and in the errors in variables linear regression model, when the distributions of the covariates and measurement errors are known.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":"77 4","pages":"563 - 596"},"PeriodicalIF":0.6000,"publicationDate":"2025-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A signed-rank estimator for nonlinear regression models when covariates and errors are dependent\",\"authors\":\"Hira L. Koul, Palaniappan Vellaisamy\",\"doi\":\"10.1007/s10463-025-00929-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This paper contains the proof of the asymptotic uniform linearity of a sequence of simple linear signed-rank statistics based on the residuals of a class of nonlinear parametric regression models, where regression errors are possibly dependent on the covariates. This result in turn is used to prove the asymptotic normality of a signed rank estimator of the regression parameter vector in the given nonlinear regression model where covariates and regression errors are dependent and in the errors in variables linear regression model, when the distributions of the covariates and measurement errors are known.</p></div>\",\"PeriodicalId\":55511,\"journal\":{\"name\":\"Annals of the Institute of Statistical Mathematics\",\"volume\":\"77 4\",\"pages\":\"563 - 596\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2025-04-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annals of the Institute of Statistical Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10463-025-00929-w\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of the Institute of Statistical Mathematics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10463-025-00929-w","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

摘要

本文利用一类非线性参数回归模型的残差证明了简单线性符号秩统计量序列的渐近一致线性性，其中回归误差可能依赖于协变量。这一结果反过来又被用来证明在给定的非线性回归模型中，当协变量和回归误差的分布已知时，回归参数向量的有符号秩估计量的渐近正态性，其中协变量和回归误差是相关的，并且在变量的线性回归模型的误差中。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

A signed-rank estimator for nonlinear regression models when covariates and errors are dependent

This paper contains the proof of the asymptotic uniform linearity of a sequence of simple linear signed-rank statistics based on the residuals of a class of nonlinear parametric regression models, where regression errors are possibly dependent on the covariates. This result in turn is used to prove the asymptotic normality of a signed rank estimator of the regression parameter vector in the given nonlinear regression model where covariates and regression errors are dependent and in the errors in variables linear regression model, when the distributions of the covariates and measurement errors are known.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Annals of the Institute of Statistical Mathematics 数学-统计学与概率论

CiteScore

2.00

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Annals of the Institute of Statistical Mathematics (AISM) aims to provide a forum for open communication among statisticians, and to contribute to the advancement of statistics as a science to enable humans to handle information in order to cope with uncertainties. It publishes high-quality papers that shed new light on the theoretical, computational and/or methodological aspects of statistical science. Emphasis is placed on (a) development of new methodologies motivated by real data, (b) development of unifying theories, and (c) analysis and improvement of existing methodologies and theories.