Some Minimax Invariant Procedures for Estimating a Cumulative Distribution Function
Om P. Aggarwal · The Annals of Mathematical Statistics · 1955
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.