• Bernoulli
  • Volume 15, Number 4 (2009), 1010-1035.

Nonparametric estimation of a convex bathtub-shaped hazard function

Hanna K. Jankowski and Jon A. Wellner

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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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Bernoulli, Volume 15, Number 4 (2009), 1010-1035.

First available in Project Euclid: 8 January 2010

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antimode bathtub consistency convex failure rate force of mortality hazard rate invelope process limit distribution nonparametric estimation U-shaped


Jankowski, Hanna K.; Wellner, Jon A. Nonparametric estimation of a convex bathtub-shaped hazard function. Bernoulli 15 (2009), no. 4, 1010--1035. doi:10.3150/09-BEJ202.

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