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March, 1973 Limiting Behavior of the Extremum of Certain Sample Functions
P. K. Sen, B. B. Bhattacharyya, M. W. Suh
Ann. Statist. 1(2): 297-311 (March, 1973). DOI: 10.1214/aos/1176342367


For a sequence of random variables forming an $m$-dependent stochastic process (not necessarily stationary), asymptotic distribution and other convergence properties of the extremum of certain functions of the empirical distribution are studied. In this context, it is shown that the asymptotic probability of the classical Kolmogorov-Smirnov statistic exceeding any positive real number provides an upper bound for the corresponding probability when the underlying random variables are not necessarily identically distributed. The theory is specifically applied to the study of the limiting distribution, strong convergence and convergence of the first moment of the strength of a bundle of parallel filaments (which is shown to be the extremum of a function of the empirical distribution).


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P. K. Sen. B. B. Bhattacharyya. M. W. Suh. "Limiting Behavior of the Extremum of Certain Sample Functions." Ann. Statist. 1 (2) 297 - 311, March, 1973.


Published: March, 1973
First available in Project Euclid: 12 April 2007

zbMATH: 0258.62010
MathSciNet: MR394989
Digital Object Identifier: 10.1214/aos/1176342367

Rights: Copyright © 1973 Institute of Mathematical Statistics


Vol.1 • No. 2 • March, 1973
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