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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Volume (Year): 61 (2003)
Issue (Month): 3 (February)
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