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

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  • Singh, R. S.

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.

Suggested Citation

  • Singh, R. S., 1979. "On necessary and sufficient conditions for uniform strong consistency of estimators of a density and its derivatives," Journal of Multivariate Analysis, Elsevier, vol. 9(1), pages 157-164, March.
    • Handle: RePEc:eee:jmvana:v:9:y:1979:i:1:p:157-164
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    Cited by:

    1. Ricardo Fraiman & Jean Meloche, 1999. "Counting Bumps," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 51(3), pages 541-569, September.

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