The limit distribution of the L-error of Grenander-type estimators

C Durot, VN Kulikov, Hendrik Paul Lopuhaä

Research output: Contribution to journalArticleScientificpeer-review


Let ƒ be a nonincreasing function defined on [0,1]. Under standard regularity conditions, we derive the asymptotic distribution of the supremum norm of the difference between ƒ and its Grenander-type estimator on sub-intervals of [0,1]. The rate of convergence is found to be of order (n/log n)−1/3 and the limiting distribution to be Gumbel.
Original languageEnglish
Pages (from-to)1578-1608
Number of pages31
JournalAnnals of Statistics
Issue number3
Publication statusPublished - 2012


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