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 $\mathscr{E}$.
Publié le : 1986-09-14
Classification:
Unimodal distribution function,
asymptotically minimax,
62E20,
62G20
@article{1176350054,
author = {Lo, Shaw-Hwa},
title = {Estimation of a Unimodal Distribution Function},
journal = {Ann. Statist.},
volume = {14},
number = {2},
year = {1986},
pages = { 1132-1138},
language = {en},
url = {http://dml.mathdoc.fr/item/1176350054}
}
Lo, Shaw-Hwa. Estimation of a Unimodal Distribution Function. Ann. Statist., Tome 14 (1986) no. 2, pp. 1132-1138. http://gdmltest.u-ga.fr/item/1176350054/