(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.
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