Lo, Shaw-Hwa Estimation of a unimodal distribution function. (English) Zbl 0611.62037 Ann. Stat. 14, 1132-1138 (1986). 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 Cited in 3 Documents MSC: 62G05 Nonparametric estimation 62G30 Order statistics; empirical distribution functions 62C20 Minimax procedures in statistical decision theory 62G20 Asymptotic properties of nonparametric inference Keywords:empirical distribution function; asymptotically minimax; unimodal distribution PDFBibTeX XMLCite \textit{S.-H. Lo}, Ann. Stat. 14, 1132--1138 (1986; Zbl 0611.62037) Full Text: DOI