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MINIMAX INVARIANT ESTIMATOR

OF A CONTINUOUS DISTRIBUTION FUNCTION

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QIQING YU

*Department of Applied Mathematics, State University of New York,*

Stony Brook, NY 11794, U.S.A.
(Received February 1, 1991; revised August 14, 1991)

**Abstract.**
Consider the problems of
the continuous invariant estimation of a
distribution function with a wide class of loss functions.
It has been conjectured for long that the best invariant estimator
is minimax for all sample sizes *n* __>__ 1.
This conjecture is proved in this short note.

*Key words and phrases*:
Minimaxity, invariant estimator,
nonparametric
estimator, product measure, Lebesgue measure, uniform distribution on a
set.

**Source**
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