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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 4, Fasc. 1,
pages 1 - 12
 

LIMIT THEOREMS FOR EMPIRICAL PROCESSES INDEXED BY CLASSES OF SETS ALLOWING A FINITE-DIMENSIONAL PARAMETRIZATION

Peter Gaenssler

Abstract: . Let q,q ,... 1 2 be independent identically distributed random variables defined on some probability space (_O_,A, P) and taking their values in a measurable space (X,B) according to the probability distribution m on B defined by m(B) := P (q (- B), 1 B (- B. Let

m := n-1(e + ...+ e ) n q1 qn
be the empirical measure on B based on q1,...qn and, given a class C < B, let

bn(C) := n1/2(mn(C) - m(C)), C (- B,
be the empirical C -process, considered as a stochastic process indexed by C. Various properties of bn as n --> oo are studied.

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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