Nonparametric estimation of a convex bathtub-shaped hazard function.
In this paper, we study the nonparametric maximum likelihood estimator (MLE) of a convex hazard function. We show that the MLE is consistent and converges at a local rate of n(2/5) at points x(0) where the true hazard function is positive and strictly convex. Moreover, we establish the pointwise asymptotic distribution theory of our estimator under these same assumptions. One notable feature of the nonparametric MLE studied here is that no arbitrary choice of tuning parameter (or complicated data-adaptive selection of the tuning parameter) is required.
Jankowski
Hanna K
HK
Department of Mathematics and Statistics, N520 Ross Building, 4700 Keele Street, York University, Toronto, ON, Canada M3J 1P3.  hkj@mathstat.yorku.ca.
Wellner
Jon A
JA
Scand Stat Theory Appl. 2008 Sep 1;35(3):385-399
19763283
J Nonparametr Stat. 2009 May 1;21(4):505-518
20300560
Bernoulli (Andover). 2009 Nov 1;15(4):1010-1035
20383267