The failure of the profile likelihood method for semi-parametric effective age models

Eric Beutner (1) , Laurent Bordes (2) , Laurent Doyen (3)

1 Department of Quantitative Economics [Maastricht]
2 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
3 FIGAL - Fiabilité et Géométrie Aléatoire

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 θ, say, exceeds the profile likelihood function evaluated at the parameter vector $\tilde\theta$, 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.

Mots clés: Cox’s proportional hazards model; Accelerated failure time model; virtual age process; Profile likelihood inference; Recurrent event data; Semi-parametric statistical model; Effective age process

Domaines: Statistiques [math.ST]

Eric Beutner, Laurent Bordes, Laurent Doyen. The failure of the profile likelihood method for semi-parametric effective age models. Bernoulli, 2017, 23 (4B), pp.3650-3684. ⟨10.3150/16-BEJ861⟩. ⟨hal-01127990⟩