随机变量加权和的完全收敛性及其在非参数回归模型中的应用

Pub Date : 2021-01-01 DOI:10.4134/JKMS.J200029

A. Shen, Yajing Zhang

{"title":"随机变量加权和的完全收敛性及其在非参数回归模型中的应用","authors":"A. Shen, Yajing Zhang","doi":"10.4134/JKMS.J200029","DOIUrl":null,"url":null,"abstract":"In this paper, we main study the strong law of large numbers and complete convergence for weighted sums of asymptotically almost negatively associated (AANA, in short) random variables, by using the Marcinkiewicz-Zygmund type moment inequality and Roenthal type moment inequality for AANA random variables. As an application, the complete consistency for the weighted linear estimator of nonparametric regression models based on AANA errors is obtained. Finally, some numerical simulations are carried out to verify the validity of our theoretical result.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"COMPLETE CONVERGENCE FOR WEIGHTED SUMS OF AANA RANDOM VARIABLES AND ITS APPLICATION IN NONPARAMETRIC REGRESSION MODELS\",\"authors\":\"A. Shen, Yajing Zhang\",\"doi\":\"10.4134/JKMS.J200029\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we main study the strong law of large numbers and complete convergence for weighted sums of asymptotically almost negatively associated (AANA, in short) random variables, by using the Marcinkiewicz-Zygmund type moment inequality and Roenthal type moment inequality for AANA random variables. As an application, the complete consistency for the weighted linear estimator of nonparametric regression models based on AANA errors is obtained. Finally, some numerical simulations are carried out to verify the validity of our theoretical result.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2021-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4134/JKMS.J200029\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4134/JKMS.J200029","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

本文主要利用AANA随机变量的Marcinkiewicz-Zygmund型矩不等式和Roenthal型矩不等式，研究了渐近几乎负相关(AANA)随机变量加权和的强大数律和完全收敛性。作为应用，得到了基于AANA误差的非参数回归模型加权线性估计量的完全一致性。最后进行了数值模拟，验证了理论结果的有效性。

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

COMPLETE CONVERGENCE FOR WEIGHTED SUMS OF AANA RANDOM VARIABLES AND ITS APPLICATION IN NONPARAMETRIC REGRESSION MODELS

In this paper, we main study the strong law of large numbers and complete convergence for weighted sums of asymptotically almost negatively associated (AANA, in short) random variables, by using the Marcinkiewicz-Zygmund type moment inequality and Roenthal type moment inequality for AANA random variables. As an application, the complete consistency for the weighted linear estimator of nonparametric regression models based on AANA errors is obtained. Finally, some numerical simulations are carried out to verify the validity of our theoretical result.

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