Necessary and sufficient conditions for weak convergence of smoothed empirical processes

Dragan Radulovic and Marten Wegkamp

Statistics & Probability Letters, 2003, vol. 61, issue 3, 321-336

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.

Keywords: Bracketing; numbers; Empirical; processes; Hellinger; differentiability; Histogram; estimators; Metric; entropy; Weak; convergence (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (2)

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