Nonparametric estimation of a convex bathtub-shaped hazard function

Details Nonparametric estimation of a convex bathtub-shaped hazard function Nonparametric estimation of a convex bathtub-shaped hazard function

2008-01-04

arxiv.org/abs/0801.0712v2

Bernoulli 2009, Vol. 15, No. 4, 1010-1035

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/09-BEJ202 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/09-BEJ202

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.

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