(Received February 23, 1996; revised May 13, 1996)
Abstract. For the invariant decision problem of estimating a continuous distribution function with the Kolmogorov-Smirnov loss within the class of `proper' distribution functions, it is proved that the sample distribution function is the best invariant estimator only for the sample size n = 1 and 2. Further it is shown that the best invariant estimator is minimax. Exact jumps of the best invariant estimator are derived for n < 4.
Key words and phrases: Best invariant estimator, Kolmogorov-Smirnov loss, minimaxity.
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