Random deletion does not affect asymptotic normality or quadratic negligibility
type: Item
instance of: scholarly article
title: Random deletion does not affect asymptotic normality or quadratic negligibility
zbMATH Open document ID: 0921.62065
author: Harry Kesten
author: Ross A. Maller
published in: Journal of Multivariate Analysis
publication date: 1999-10-05T00:00:00Z
review text: A sample of random vectors \(X_i\) is considered. The main theorem gives six equivalent conditions for a deletion scheme, for which the number of deleted points is bounded in probability, as the sample size \(n\to\infty\). The sample sum of the ``trimmed'' sample is asymptotically normal (after norming and centering) if and only if the original sample sum is asymptotically normal (with the same norming and centering). The original sample must be drawn from a distribution in the domain of attraction of the multivariate normal distribution. Let be \(V_n=\sum^n_{i=1} X_iX_i^T\). The \(X_i\) are quadratic negligible if \(\max_nX^T_iV_n^{-1}X_i @>P>>0\), \(1\leq i\leq n\), \(n\to\infty\). The random deletion has no effect on the quadratic neglibility. The quadratic neglibility of the deleted sample belongs to the conditions of the main theorem.
Mathematics Subject Classification ID: 62H10
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 62H12
Mathematics Subject Classification ID: 62J05
Mathematics Subject Classification ID: 62E20
zbMATH DE Number: 1085313
zbMATH Keywords: asymptotic normality
zbMATH Keywords: random deletion of observations
zbMATH Keywords: domain of attraction
zbMATH Keywords: normal distribution
zbMATH Keywords: quadratic neglibility
reviewed by: Pavel Froněk
MaRDI profile type: Publication
full work available at URL: jmva.1997.1698
OpenAlex ID: W2069393075
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DOI: 10.1006/JMVA.1997.1698
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description: scientific article; zbMATH DE number 1085313