Necessary and sufficient conditions for weak convergence of smoothed empirical processes

Let X1,...,Xn be a sequence of i.i.d. random variables with common distribution P on the real line. Assuming that P has a smooth density, we construct a histogram based estimator Pn,H and establish weak convergence of the empirical process under sharp conditions. If is a class of indicators of sets, then the conditions imposed are necessary and sufficient.

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Year of publication:	2003
Authors:	Radulovic, Dragan ; Wegkamp, Marten
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 61.2003, 3, p. 321-336
Publisher:	Elsevier
Keywords:	Bracketing numbers Empirical processes Hellinger differentiability Histogram estimators Metric entropy Weak convergence

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005074772