Estimation of a Unimodal Distribution Function
The Annals of Statistics · 1986 · Volume 14 · Issue 3
Abstract
This paper deals with the problem of efficiently estimating (asymptotically minimax) a distribution function when essentially nothing is known about it except that it is unimodal. The sample distribution function $F_n$ is shown to be asymptotically minimax among the family $\mathscr{E}$ of all unimodal distribution functions. Since $F_n$ does not belong to this family, estimators belonging to this family are constructed and are shown to be asymptotically minimax relative to the collection of subfamilies of $\mathscr{E}$.
Keywords
62E20, 62G20, asymptotically minimax, unimodal distribution function
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