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International Journal of Stochastic Analysis

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International Journal of Stochastic Analysis / 1994 / Article

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Volume 7 |Article ID 574048 | https://doi.org/10.1155/S1048953394000146

Rimas Norvaiša, "Laws of large numbers for L-statistics", International Journal of Stochastic Analysis, vol. 7, Article ID 574048, 19 pages, 1994. https://doi.org/10.1155/S1048953394000146

Laws of large numbers for L-statistics

Rimas Norvaiša1

1Institute of Mathematics and Informatics, Akademijos 4, Lithuania

Received01 Feb 1992
Revised01 Apr 1994

Abstract

Consider Ln=n−1∑1≤i≤ncnig(Xn:i) for order statistics Xn:i and let cni=n∫(i−1)/ni/nJdλ for some (Lebesgue) λ-summable over (0,1) function J. Sufficient as well as necessary conditions for limnLn=∫01Jgdλ to hold almost surely and in probability are given. Superposition (or Nemytskii) operators have been used to derive the laws of large numbers for L-statistics from the laws of large numbers in quasi-Banach function spaces for the empirical distribution functions based on X1,…,Xn.

Copyright © 1994 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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