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Estimation of a unimodal distribution function. (English) Zbl 0611.62037
Author’s summary: 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 $${\mathcal E}$$ 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 $${\mathcal E}$$.
Reviewer: Zhao Lincheng

MSC:
 62G05 Nonparametric estimation 62G30 Order statistics; empirical distribution functions 62C20 Minimax procedures in statistical decision theory 62G20 Asymptotic properties of nonparametric inference
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