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September, 1986 Estimation of a Unimodal Distribution Function
Shaw-Hwa Lo
Ann. Statist. 14(3): 1132-1138 (September, 1986). DOI: 10.1214/aos/1176350054

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 $\mathscr{E}$.

Citation

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Shaw-Hwa Lo. "Estimation of a Unimodal Distribution Function." Ann. Statist. 14 (3) 1132 - 1138, September, 1986. https://doi.org/10.1214/aos/1176350054

Information

Published: September, 1986
First available in Project Euclid: 12 April 2007

zbMATH: 0611.62037
MathSciNet: MR856810
Digital Object Identifier: 10.1214/aos/1176350054

Subjects:
Primary: 62E20
Secondary: 62G20

Rights: Copyright © 1986 Institute of Mathematical Statistics

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Vol.14 • No. 3 • September, 1986
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