{"title":"Limit Joint Distribution of $$\\boldsymbol{U}$$ -Statistics, $$\\boldsymbol{M}$$ -Estimates, and Sample Quantiles","authors":"M. P. Savelov","doi":"10.3103/s0027132223060074","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Let <span>\\(X_{1},X_{2},\\ldots,X_{n}\\)</span> be independent identically distributed random vectors. Consider a vector <span>\\(V(X_{1},X_{2},\\ldots,X_{n})\\)</span> whose each component is either a <span>\\(U\\)</span>-statistic or an <span>\\(M\\)</span>-estimator. Sufficient conditions for asymptotic normality of the vector <span>\\(V(X_{1},X_{2},\\ldots,X_{n})\\)</span> are obtained. In the case when <span>\\(X_{1},X_{2},\\ldots\\)</span> are one-dimensional, sufficient conditions for asymptotic normality are obtained for a vector, each component of which is either a <span>\\(U\\)</span>-statistic, or an <span>\\(M\\)</span>-estimator, or a sample quantile.</p>","PeriodicalId":42963,"journal":{"name":"Moscow University Mathematics Bulletin","volume":null,"pages":null},"PeriodicalIF":0.2000,"publicationDate":"2024-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Moscow University Mathematics Bulletin","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3103/s0027132223060074","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Let \(X_{1},X_{2},\ldots,X_{n}\) be independent identically distributed random vectors. Consider a vector \(V(X_{1},X_{2},\ldots,X_{n})\) whose each component is either a \(U\)-statistic or an \(M\)-estimator. Sufficient conditions for asymptotic normality of the vector \(V(X_{1},X_{2},\ldots,X_{n})\) are obtained. In the case when \(X_{1},X_{2},\ldots\) are one-dimensional, sufficient conditions for asymptotic normality are obtained for a vector, each component of which is either a \(U\)-statistic, or an \(M\)-estimator, or a sample quantile.
AbstractLet \(X_{1},X_{2},\ldots,X_{n}\) are independent identically distributed random vector.考虑一个向量 \(V(X_{1},X_{2},\ldots,X_{n}))，它的每个分量都是\(U\)-统计量或\(M\)-估计量。得到了向量 \(V(X_{1},X_{2},\ldots,X_{n})\)渐近正态性的充分条件。在\(X_{1},X_{2},\ldots\)是一维的情况下，得到了向量渐近正态性的充分条件，该向量的每个分量要么是一个\(U\)-统计量，要么是一个\(M\)-估计量，要么是一个样本量位数。
期刊介绍：
Moscow University Mathematics Bulletin is the journal of scientific publications reflecting the most important areas of mathematical studies at Lomonosov Moscow State University. The journal covers research in theory of functions, functional analysis, algebra, geometry, topology, ordinary and partial differential equations, probability theory, stochastic processes, mathematical statistics, optimal control, number theory, mathematical logic, theory of algorithms, discrete mathematics and computational mathematics.
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