COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1683 Estimation and Model Selection of Semiparametric Multivariate
Survival Functions Xiaohong Chen, Yanqin Fan, Demian Pouzo, and Zhiliang Ying November 2008 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. |
