Open AccessThe failure of the profile likelihood method for a large class of semi-parametric models
Author(s) -
Eric Beutner,
Laurent Bordes,
Laurent Doyen
Publication year - 2017
Publication title -
bernoulli
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.814
H-Index - 72
eISSN - 1573-9759
pISSN - 1350-7265
DOI - 10.3150/16-bej861
Subject(s) - mathematics , parametric statistics , parametric model , likelihood function , monotone polygon , function (biology) , inference , restricted maximum likelihood , maximum likelihood , semiparametric model , statistics , computer science , geometry , evolutionary biology , artificial intelligence , biology
International audienceWe 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