On necessary and sufficient conditions for uniform strong consistency of estimators of a density and its derivatives

R. S. Singh

Journal of Multivariate Analysis, 1979, vol. 9, issue 1, 157-164

Abstract: Based on a random sample from a population with (unknown) probability density f, this note exhibits a class of statistics f(p) for each fixed integer p [greater, double equals] 0. It is shown that f(p) are uniformly strongly consistent estimators of f(p), the pth order derivative of f, if and only if f(p) is bounded and uniformly continuous.

Keywords: Density; pth-order; derivative; of; a; density; strong; consistency; uniform; continuity (search for similar items in EconPapers)
Date: 1979
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