Centre for Mathematical Physics and Stochastics

Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

MPS-LN 1999-4

August 1999

From the preface:

These lecture notes begin with a chapter on the classical empirical process defined in terms of empirical distribution functions. A proof, expanding on one in a 1989 paper by Bretagnolle and Massart, is given for the Komlos-Major-Tusnady result on the speed of convergence of the empirical process to a Brownian bridge in the supremum norm. The rest of the notes are about the theory of empirical processes on general spaces, and are an abridgment of my book, Uniform Central Limit Theorems, or "UCLT", to be published by Cambridge University Press. In this abridgment, proofs are not given except for some very short ones and some not given in UCLT.

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