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March, 1985 The Admissibility of the Empirical Distribution Function
Michael P. Cohen, Lynn Kuo
Ann. Statist. 13(1): 262-271 (March, 1985). DOI: 10.1214/aos/1176346591

Abstract

Consider the problem of estimating an unknown distribution function $F$ from the class of all distribution functions given a random sample of size $n$ from $F$. It is proved that the empirical distribution function is admissible for the loss functions $L(F, \hat{F}) = \int (\hat{F}(t) - F(t))^2(F(t))^\alpha(1 - F(t))^b dW(t)$ for any $a < 1$ and $b < 1$ and finite measure $W$. Related results for simultaneous estimation of distribution functions and for finite population sampling are also given.

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Michael P. Cohen. Lynn Kuo. "The Admissibility of the Empirical Distribution Function." Ann. Statist. 13 (1) 262 - 271, March, 1985. https://doi.org/10.1214/aos/1176346591

Information

Published: March, 1985
First available in Project Euclid: 12 April 2007

zbMATH: 0575.62011
MathSciNet: MR773166
Digital Object Identifier: 10.1214/aos/1176346591

Subjects:
Primary: 62C15
Secondary: 62D05, 62G30

Rights: Copyright © 1985 Institute of Mathematical Statistics

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Vol.13 • No. 1 • March, 1985
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