On accuracy of approximation in Koul's Theorem for weighted empirical processes

Alexander Sakhanenko, Novosibirsk State University, Sobolev Institute of Mathematics, Novosibirsk, Russia

Using coupling we obtain estimates for the distribution of the uniform distance between a given weighted empirical process and an accompanying gaussian process, with the same mean and covariance function. For such weighted empirical processes in the book, Hira L. Koul “Weighted Empirical Processes in Dynamic Nonlinear Models” was only established weak convergence of distributions. However, our estimates do not require the continuity of the limiting Gaussian process. They are also valid for the uniform norm. This is a joint work with O.A. Sukhovershina.

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