The Annals of Statistics

The Admissibility of the Empirical Distribution Function

Michael P. Cohen and Lynn Kuo

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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.

Article information

Source
Ann. Statist., Volume 13, Number 1 (1985), 262-271.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176346591

Digital Object Identifier
doi:10.1214/aos/1176346591

Mathematical Reviews number (MathSciNet)
MR773166

Zentralblatt MATH identifier
0575.62011

JSTOR
links.jstor.org

Subjects
Primary: 62C15: Admissibility
Secondary: 62G30: Order statistics; empirical distribution functions 62D05: Sampling theory, sample surveys

Keywords
Admissibility empirical distribution function i.i.d. sample weighted quadratic loss simple random sampling without replacement finite population multinomial distribution

Citation

Cohen, Michael P.; Kuo, Lynn. The Admissibility of the Empirical Distribution Function. Ann. Statist. 13 (1985), no. 1, 262--271. doi:10.1214/aos/1176346591. https://projecteuclid.org/euclid.aos/1176346591


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