THE LIMIT DISTRIBUTION OF THE L.-ERROR OF GRENANDER-TYPE ESTIMATORS

Authors
Cécile Durot Vladimir N. Kulikov Hendrik P. Lopuhaä
Citation
Cécile Durot et al., THE LIMIT DISTRIBUTION OF THE L.-ERROR OF GRENANDER-TYPE ESTIMATORS, Annals of statistics , 40(3), 2012, pp. 1578-1608
Journal title
Annals of statistics → ACNP
ISSN journal
00905364
Volume
40
Issue
3
Year of publication
2012
Pages
1578 - 1608
Database
ACNP
SICI code
Abstract
Let . 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 . 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.