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
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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 -