Convergence of the CUSUM estimation for a mean shift in linear processes with random coefficients

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-02-12 DOI:10.1007/s00180-024-01465-6

Yi Wu, Wei Wang, Xuejun Wang

引用次数: 0

Abstract

Let \(\{X_{i},1\le i\le n\}\) be a sequence of linear process based on dependent random variables with random coefficients, which has a mean shift at an unknown location. The cumulative sum (CUSUM, for short) estimator of the change point is studied. The strong convergence, \(L_{r}\) convergence, complete convergence and the rate of strong convergence are established for the CUSUM estimator under some mild conditions. These results improve and extend the corresponding ones in the literature. Simulation studies and two real data examples are also provided to support the theoretical results.

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具有随机系数的线性过程中均值移动的 CUSUM 估计的收敛性

设（\{X_{i},1\le i\le n\}\ ）是一个基于因变量的线性过程序列，具有随机系数，在未知位置有均值移动。研究了变化点的累积和（简称 CUSUM）估计器。在一些温和的条件下，建立了 CUSUM 估计器的强收敛性、（L_{r}\）收敛性、完全收敛性和强收敛率。这些结果改进并扩展了文献中的相应结果。此外，还提供了仿真研究和两个真实数据实例来支持理论结果。

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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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.

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