Kiefer's Law of the iterated logarithm of the vector of upper order statistics

Vasudeva, R. and Moridani, A. (2015) Kiefer's Law of the iterated logarithm of the vector of upper order statistics. PROBABILITY AND MATHEMATICAL STATISTICS-POLAND, 31 (2). pp. 331-347. ISSN 0974-3235

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Abstract

Let {X-n} be a sequence of independent identically distributed random variables with a common continuous distribution function and let M-j,(n) denote the jth upper order statistic among X-1, X-2, ... , X-n, n >= j. For a large class of distributions, we obtain the law of the iterated logarithm for {M-1, (n), M-2,(n)}, properly normalized. As a consequence, we establish a law of the iterated logarithm for the spacings {M-1,(n) - M-2,(n)}.

Item Type: Article
Uncontrolled Keywords: Law of the iterated logarithm; upper order statistics; regularly varying function
Subjects: E Mathematical Science > Statistics
Divisions: Department of > Statistics
Depositing User: lpa venkatesh user
Date Deposited: 14 Jun 2019 07:32
Last Modified: 14 Jun 2019 07:32
URI: http://eprints.uni-mysore.ac.in/id/eprint/2587

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