Nonparametric estimation of a convex bathtub-shaped hazard function
Hanna K. Jankowski and Jon A. Wellner
Source: Bernoulli Volume 15, Number 4
(2009), 1010-1035.
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 n2/5 at points x0 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.
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Keywords: antimode; bathtub; consistency; convex; failure rate; force of mortality; hazard rate; invelope process; limit distribution; nonparametric estimation; U-shaped
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.bj/1262962224
Digital Object Identifier: doi:10.3150/09-BEJ202
Mathematical Reviews number (MathSciNet): MR2597581
Zentralblatt MATH identifier: 1200.62025
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