Komlos-Major-Tusnady approximation for the general empirical process and Haar expansions of classes of functions |
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| Authors: | Vladimir I. Koltchinskii |
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| Affiliation: | (1) Department of Probability and Statistics, Kiev State University, 252017 Kiev, Ukraine;(2) Department of Mathematics, University of Connecticut, 06269-3009 Storrs, Connecticut |
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| Abstract: | Rates of convergence of the Komlos-Major-Tusnady type in the invariance principle for empirical processes indexed by functions are obtained. The conditions are given in terms of the empirical entropy and the accuracy of the Haar type approximation for the corresponding classes of functions. The recent results of Massart(25) as well as some new results for empirical characteristic functions are obtained as a corollary. |
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| Keywords: | Empirical processes KMT-approximation Brownian bridge empirical entropy Haar basis |
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