title: Nonparametric estimation of a convex bathtub-shaped hazard function.
abstract: 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.
authors.affiliation: Department of Mathematics and Statistics, N520 Ross Building, 4700 Keele Street, York University, Toronto, ON, Canada M3J 1P3.  hkj@mathstat.yorku.ca.
authors.forename: Hanna K
authors.initials: HK
authors.lastname: Jankowski
authors.forename: Jon A
authors.initials: JA
authors.lastname: Wellner
references.citation: Scand Stat Theory Appl. 2008 Sep 1;35(3):385-399
references.pmid: 19763283
references.citation: J Nonparametr Stat. 2009 May 1;21(4):505-518
references.pmid: 20300560
references.citation: Bernoulli (Andover). 2009 Nov 1;15(4):1010-1035
references.pmid: 20383267