You can manage bookmarks using lists, please log in to your user account for this.
Media type:
E-Article
Title:
Strong Laws for Quantiles Corresponding to Moving Blocks of Random Variables
Contributor:
Russo, Ralph P.
Published:
Institute of Mathematical Statistics, 1988
Published in:
The Annals of Probability, 16 (1988) 1, Seite 162-171
Language:
English
ISSN:
0091-1798
Origination:
Footnote:
Description:
Let U1, U2,... be a sequence of independent uniform (0, 1) random variables, and for 1 ≤ k ≤ n let ξp(n, k) denote the pth quantile,$0 < p < 1$, corresponding to the block Un -k + 1,...,Un. In this paper we investigate the a.s. limiting behavior of ξp(n, an) when anis an integer sequence, 1 ≤ an≤ 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 maxan≤ k ≤ nξp(n, k) and other maxima involving the ξp(n, k)'s.