Abstract
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 language | English |
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Pages (from-to) | 1578-1608 |
Number of pages | 31 |
Journal | Annals of Statistics |
Volume | 40 |
Issue number | 3 |
DOIs | |
Publication status | Published - 2012 |