TY - JOUR

T1 - The failure of the profile likelihood method for a large class of semi-parametric models

AU - Beutner, Eric

AU - Bordes, Laurent

AU - Doyen, Laurent

PY - 2017/11/1

Y1 - 2017/11/1

N2 - 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 θ , 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.

AB - 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 θ , 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.

KW - Cox's proportional hazards model

KW - Eccelerated failure time model

KW - Effective age process

KW - Profile likelihood inference

KW - Recurrent event data

KW - Semi-parametric statistical model

KW - Virtual age process

UR - http://www.scopus.com/inward/record.url?scp=85019638132&partnerID=8YFLogxK

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U2 - 10.3150/16-BEJ861

DO - 10.3150/16-BEJ861

M3 - Article

AN - SCOPUS:85019638132

VL - 23

SP - 3650

EP - 3684

JO - Bernoulli: A Journal of Mathematical Statistics and Probability

JF - Bernoulli: A Journal of Mathematical Statistics and Probability

SN - 1350-7265

IS - 4B

ER -