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Necessary and sufficient conditions for weak convergence of smoothed empirical processes

✍ Scribed by Dragan Radulović; Marten Wegkamp

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
200 KB
Volume
61
Category
Article
ISSN
0167-7152

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✦ Synopsis

Let X 1 ; : : : ; X n 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 P n; H and establish weak convergence of the empirical process √ n(P n; H -P)(f) f∈F under sharp conditions. If F is a class of indicators of sets, then the conditions imposed are necessary and su cient.

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