{"title":"A Berry–Esseen theorem for sample quantiles under martingale difference sequences","authors":"Chao Lu, Houlin Zhou, Xuejun Wang","doi":"10.1080/02331888.2023.2225668","DOIUrl":null,"url":null,"abstract":"In this paper, we establish the uniformly asymptotic normality for sample quantiles based on martingale difference sequences under some suitable conditions. We obtain the rate of normality approximation of by using some classical methods such as Bernstein type inequality, and so on. Finally, we verify asymptotic normality for the fixed quantile of the martingale difference sequences and present some numerical simulations to demonstrate the finite sample performances of the theoretical results.","PeriodicalId":54358,"journal":{"name":"Statistics","volume":"46 1","pages":"844 - 866"},"PeriodicalIF":1.2000,"publicationDate":"2023-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/02331888.2023.2225668","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we establish the uniformly asymptotic normality for sample quantiles based on martingale difference sequences under some suitable conditions. We obtain the rate of normality approximation of by using some classical methods such as Bernstein type inequality, and so on. Finally, we verify asymptotic normality for the fixed quantile of the martingale difference sequences and present some numerical simulations to demonstrate the finite sample performances of the theoretical results.
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.
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