publication . Article . Other literature type . 1990

The Asymptotic Joint Distribution of Self-Normalized Censored Sums and Sums of Squares

James Kuelbs; Marjorie G. Hahn; Daniel C. Weiner;
Open Access
  • Published: 01 Jul 1990 Journal: The Annals of Probability, volume 18, pages 1,284-1,341 (issn: 0091-1798, Copyright policy)
  • Publisher: Institute of Mathematical Statistics
Abstract
Empirical versions of appropriate centering and scale constants for random variables which can fail to have second or even first moments are obtainable in various ways via suitable modifications of the summands in the partial sum. This paper discusses a particular modification, called censoring (which is a kind of winsorization), where the (random) number of summands altered tends to infinity but the proportion altered tends to zero as the number of summands increases. Some analytic advantages inherent in this approach allow a fairly complete probabilistic and empirical theory to be developed, the latter involving the study of studentized or self-normalized sums...
Subjects
free text keywords: Statistics, Probability and Uncertainty, Statistics and Probability, Asymptotic normality, self-normalized sums, censoring, Feller class, stochastic compactness, tightness, center and scale constants, infinite variance, domain of attraction, 60F05, 62G05, 62G30, Applied mathematics, Combinatorics, Censoring (statistics), Probabilistic logic, Joint probability distribution, Mathematics, Winsorizing, Random variable, Studentization, Asymptotic distribution, Studentized range
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