一类随机变量加权和的弱收敛性及其相关的统计应用

IF 1.2 4区数学 Q2 STATISTICS & PROBABILITY

Statistics Pub Date : 2023-06-27 DOI:10.1080/02331888.2023.2227984

S. Zheng, Fei Zhang, Chunhua Wang, Xuejun Wang

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引用次数: 0

摘要

本文研究了一类满足Rosenthal型不等式的随机变量加权和的弱大数律的弱收敛性和收敛速率。给出了在温和条件下弱大数律收敛速率的充分必要条件。此外，我们建立的主要结果应用于简单的线性变量误差回归模型和基于一类随机误差的非参数回归模型。最后，我们给出了一些数值模拟来评估理论结果的有限样本性能。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Weak convergence for weighted sums of a class of random variables with related statistical applications

In this paper, we study the weak convergence and convergence rate in the weak law of large numbers for weighted sums of a class of random variables satisfying the Rosenthal type inequality. The necessary and sufficient conditions for the convergence rates in the weak law of large numbers under some mild conditions are provided. Moreover, the main results that we established are applied to simple linear errors-in-variables regression models and nonparametric regression models based on a class of random errors. Finally, we present some numerical simulations to assess the finite sample performance of the theoretical results.

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来源期刊

Statistics 数学-统计学与概率论

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

12 months

期刊介绍： Statistics publishes papers developing and analysing new methods for any active field of statistics, motivated by real-life problems. Papers submitted for consideration should provide interesting and novel contributions to statistical theory and its applications with rigorous mathematical results and proofs. Moreover, numerical simulations and application to real data sets can improve the quality of papers, and should be included where appropriate. Statistics does not publish papers which represent mere application of existing procedures to case studies, and papers are required to contain methodological or theoretical innovation. Topics of interest include, for example, nonparametric statistics, time series, analysis of topological or functional data. Furthermore the journal also welcomes submissions in the field of theoretical econometrics and its links to mathematical statistics.