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November 2017 The failure of the profile likelihood method for a large class of semi-parametric models
Eric Beutner, Laurent Bordes, Laurent Doyen
Bernoulli 23(4B): 3650-3684 (November 2017). DOI: 10.3150/16-BEJ861

Abstract

We consider a semi-parametric model for recurrent events. The model consists of an unknown hazard rate function, the infinite-dimensional parameter of the model, and a parametrically specified effective age function. We will present a condition on the family of effective age functions under which the profile likelihood function evaluated at the parameter vector $\mathbf{{\theta}}$, say, exceeds the profile likelihood function evaluated at the parameter vector $\tilde{\boldsymbol {\theta}}$, say, with probability $p$. From this we derive a condition under which profile likelihood inference for the finite-dimensional parameter of the model leads to inconsistent estimates. Examples will be presented. In particular, we will provide an example where the profile likelihood function is monotone with probability one regardless of the true data generating process. We also discuss the relation of our results to other semi-parametric models like the accelerated failure time model and Cox’s proportional hazards model.

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Eric Beutner. Laurent Bordes. Laurent Doyen. "The failure of the profile likelihood method for a large class of semi-parametric models." Bernoulli 23 (4B) 3650 - 3684, November 2017. https://doi.org/10.3150/16-BEJ861

Information

Received: 1 February 2015; Revised: 1 April 2016; Published: November 2017
First available in Project Euclid: 23 May 2017

zbMATH: 06778299
MathSciNet: MR3654819
Digital Object Identifier: 10.3150/16-BEJ861

Rights: Copyright © 2017 Bernoulli Society for Mathematical Statistics and Probability

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Vol.23 • No. 4B • November 2017
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