On the strong law of large numbers for L-statistics with dependent data

Abstract

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

6 pages. Accepted for publication in Siberian Math. Journal. See also http://www.nsu.ru/mmf/tvims/baklanov/baklanov.html