{"title":"On the consistency of the jackknife estimator of the asymptotic variance of spatial median","authors":"František Rublík","doi":"10.1016/j.jmva.2024.105399","DOIUrl":null,"url":null,"abstract":"<div><div>It is shown that the usual delete-1 jackknife variance estimator of the asymptotic variance of spatial median is consistent. This is proved under the assumptions that the dimension of the data <span><math><mrow><mi>d</mi><mo>≥</mo><mn>3</mn></mrow></math></span>, the sampled distribution possesses a density with respect to the Lebesgue measure and this density is bounded on every bounded subset of <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"207 ","pages":"Article 105399"},"PeriodicalIF":1.4000,"publicationDate":"2024-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Multivariate Analysis","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0047259X24001064","RegionNum":3,"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
It is shown that the usual delete-1 jackknife variance estimator of the asymptotic variance of spatial median is consistent. This is proved under the assumptions that the dimension of the data , the sampled distribution possesses a density with respect to the Lebesgue measure and this density is bounded on every bounded subset of .
期刊介绍：
Founded in 1971, the Journal of Multivariate Analysis (JMVA) is the central venue for the publication of new, relevant methodology and particularly innovative applications pertaining to the analysis and interpretation of multidimensional data.
The journal welcomes contributions to all aspects of multivariate data analysis and modeling, including cluster analysis, discriminant analysis, factor analysis, and multidimensional continuous or discrete distribution theory. Topics of current interest include, but are not limited to, inferential aspects of
Copula modeling
Functional data analysis
Graphical modeling
High-dimensional data analysis
Image analysis
Multivariate extreme-value theory
Sparse modeling
Spatial statistics.
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