A note on uniform strong convergence of bivariate density estimates |
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Authors: | M. Samanta |
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Affiliation: | 1. Department of Statistics, University of Manitoba, Winnipeg, Manitoba, Canada
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Abstract: | In this paper we consider a class of estimates of a bivariate density function f based on an independent sample of size n. Under the assumption that f is uniformly continuous, the uniform strong consistency of such estimates was first proved by Nadaraya (1970) for a large class of kernel functions. In this note we show that the assumption of the uniform continuity of f is necessary for this type of convergence. |
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