This article is cited in 5 papers

The strong law of large numbers for $L$-statistics with dependent data

E. A. Baklanov

Novosibirsk State University

Abstract: We prove the strong law of large numbers for the linear combinations of functions of order statistics ($L$-statistics) based on weakly dependent random variables. We also establish the Glivenko–Cantelli theorem for $\varphi$-mixing sequences of identically distributed random variables.

Keywords: $L$-statistics, stationary ergodic sequences, $\varphi$-mixing, Glivenko–Cantelli theorem, strong law of large numbers.

UDC: 519.214

Received: 23.03.2006
Revised: 31.05.2006

 English version: Siberian Mathematical Journal, 2006, 47:6, 974–979

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