Canadian Journal of Statistics

The strong uniform convergence of multivariate variable kernel estimates

Journal Article

Abstract

We show that sup, completely as, where f is a uniformly continuous density on are independent random vectors with common density f, and fn is the variable kernel estimate

Here Hni is the distance between Xi and its kth nearest neighbour, K is a given density satisfying some regularity conditions, and k is a sequence of integers with the property that log asn

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