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January, 1988 Strong Laws for Quantiles Corresponding to Moving Blocks of Random Variables
Ralph P. Russo
Ann. Probab. 16(1): 162-171 (January, 1988). DOI: 10.1214/aop/1176991891

Abstract

Let $U_1, U_2,\ldots$ be a sequence of independent uniform (0, 1) random variables, and for $1 \leq k \leq n$ let $\xi_p(n, k)$ denote the $p$th quantile, $0 < p < 1$, corresponding to the block $U_{n -k + 1},\ldots,U_n$. In this paper we investigate the a.s. limiting behavior of $\xi_p(n, a_n)$ when $a_n$ is an integer sequence, $1 \leq a_n \leq n$, and $\lim_{n \rightarrow \infty}a_n/\log n = \beta \in \lbrack 0, \infty\rbrack$. In addition, we investigate the a.s. limiting behavior of $\max_{a_n \leq k \leq n}\xi_p(n, k)$ and other maxima involving the $\xi_p(n, k)$'s.

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Ralph P. Russo. "Strong Laws for Quantiles Corresponding to Moving Blocks of Random Variables." Ann. Probab. 16 (1) 162 - 171, January, 1988. https://doi.org/10.1214/aop/1176991891

Information

Published: January, 1988
First available in Project Euclid: 19 April 2007

zbMATH: 0636.60028
MathSciNet: MR920261
Digital Object Identifier: 10.1214/aop/1176991891

Subjects:
Primary: 60F15
Secondary: 62G30

Keywords: Erdos-Renyi laws , laws of large numbers , quantiles

Rights: Copyright © 1988 Institute of Mathematical Statistics

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Vol.16 • No. 1 • January, 1988
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