This article is cited in 1 paper

Probability theory and mathematical statistics

On accuracy of approximation in Koul’s theorem for weighted empirical processes

A. I. Sakhanenko^a, O. A. Sukhovershina<sup>b

a</sup> Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
^b Novosibirsk State University, str. Pirogova, 2, 630090, Novosibirsk, Russia

Abstract: Using coupling we obtain an estimate for the distribution of the uniform distance between a given weighted empirical process and an accompanying gaussian process with the same mean and the covariance function. This estimate also allows us to obtain Koul’s theorem under more general sufficient assumptions.

Keywords: weighted empirical processes, gaussian approximation, accuracy of approximation, coupling, accompanying gaussian processes.

UDC: 519.21

MSC: 62G30

Received September 28, 2015, published November 6, 2015

DOI: 10.17377/semi.2015.12.064