Estimation and Model Selection of Semiparametric Multivariate Survival Functions under General Censorship

Many models of semiparametric multivariate survival functions are characterized by nonparametric marginal survival functions and parametric copula functions, where different copulas imply different dependence structures. This paper considers estimation and model selection for these semiparametric multivariate survival functions, allowing for misspecified parametric copulas and data subject to general censoring. We first establish convergence of the two-step estimator of the copula parameter to the pseudo-true value defined as the value of the parameter that minimizes the KLIC between the parametric copula induced multivariate density and the unknown true density. We then derive its root--n asymptotically normal distribution and provide a simple consistent asymptotic variance estimator by accounting for the impact of the nonparametric estimation of the marginal survival functions. These results are used to establish the asymptotic distribution of the penalized pseudo-likelihood ratio statistic for comparing multiple semiparametric multivariate survival functions subject to copula misspecification and general censorship. An empirical application of the model selection test to the Loss-ALAE insurance data set is provided.Multivariate survival models, Misspecified copulas, Penalized pseudo-likelihood ratio, Fixed or random censoring, Kaplan-Meier estimator