title: Likelihood ratio procedures and tests of fit in parametric and semiparametric copula models with censored data.
abstract: Copula models for multivariate lifetimes have become widely used in areas such as biomedicine, finance and insurance. This paper fills some gaps in existing methodology for copula parameters and model assessment. We consider procedures based on likelihood and pseudolikelihood ratio statistics and introduce semiparametric maximum likelihood estimation leading to semiparametric versions. For cases where standard asymptotic approximations do not hold, we propose an efficient simulation technique for obtaining p-values. We apply these methods to tests for a copula model, based on embedding it in a larger copula family. It is shown that the likelihood and pseudolikelihood ratio tests are consistent even when the expanded copula model is misspecified. Power comparisons with two other tests of fit indicate that model expansion provides a convenient, powerful and robust approach. The methods are illustrated on an application concerning the time to loss of vision in the two eyes of an individual.
authors.affiliation: Prosserman Centre for Health Research, Samuel Lunenfeld Research Institute, Mount Sinai Hospital, Toronto, ON, Canada. yilmaz@lunenfeld.ca
authors.forename: Yildiz E
authors.initials: YE
authors.lastname: Yilmaz
authors.forename: Jerald F
authors.initials: JF
authors.lastname: Lawless
mesh_terms: D001699:Biometry / Q000379:methods*; D003198:Computer Simulation; D003930:Diabetic Retinopathy / Q000628:therapy; D006801:Humans; D008028:Light Coagulation / Q000592:standards; D016013:Likelihood Functions; D008954:Models, Biological; D015233:Models, Statistical; D014792:Visual Acuity