Some Minimax Invariant Procedures for Estimating a Cumulative Distribution Function

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Abstract
Some invariant procedures, which are essentially step-functions, are considered as estimators of the cumulative distribution function of a one-dimensional random variable on which a finite fixed number of observations are given, for various loss functions. Two principal classes of loss functions are considered and it is shown that for a special loss function in one class the optimum procedure is the usual sample cumulative function.

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