## Bernoulli

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

### 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.

#### Article information

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

Dates
First available in Project Euclid: 8 January 2010

https://projecteuclid.org/euclid.bj/1262962224

Digital Object Identifier
doi:10.3150/09-BEJ202

Mathematical Reviews number (MathSciNet)
MR2597581

Zentralblatt MATH identifier
1200.62025

#### Citation

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. https://projecteuclid.org/euclid.bj/1262962224

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