## Bernoulli

• Bernoulli
• Volume 23, Number 4B (2017), 3650-3684.

### The failure of the profile likelihood method for a large class of semi-parametric models

#### 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.

#### Article information

Source
Bernoulli, Volume 23, Number 4B (2017), 3650-3684.

Dates
Revised: April 2016
First available in Project Euclid: 23 May 2017

https://projecteuclid.org/euclid.bj/1495505105

Digital Object Identifier
doi:10.3150/16-BEJ861

Mathematical Reviews number (MathSciNet)
MR3654819

Zentralblatt MATH identifier
06778299

#### Citation

Beutner, Eric; Bordes, Laurent; Doyen, Laurent. The failure of the profile likelihood method for a large class of semi-parametric models. Bernoulli 23 (2017), no. 4B, 3650--3684. doi:10.3150/16-BEJ861. https://projecteuclid.org/euclid.bj/1495505105

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