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Necessary and sufficient conditions for weak convergence of smoothed empirical processes

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Author Info
Radulovic, Dragan
Wegkamp, Marten
Abstract

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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Article provided by Elsevier in its journal Statistics & Probability Letters.

Volume (Year): 61 (2003)
Issue (Month): 3 (February)
Pages: 321-336
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Handle: RePEc:eee:stapro:v:61:y:2003:i:3:p:321-336

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Keywords: Bracketing numbers Empirical processes Hellinger differentiability Histogram estimators Metric entropy Weak convergence;

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  1. Victor Chernozhukov & Ivan Fernandez-Val & Blaise Melly, 2009. "Inference on counterfactual distributions," CeMMAP working papers CWP09/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
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