Calibration estimation of semiparametric copula models with data missing at random

Abstract

This paper investigates the estimation of semiparametric copula models with data missing at random. The maximum pseudo-likelihood estimation of Genest et al. (1995) is infeasible if there are missing data. We propose a class of calibration estimators for the nonparametric marginal distributions and the copula parameters of interest by balancing the empirical moments of covariates between observed and whole groups. Our proposed estimators do not require the estimation of the missing mechanism, and they enjoy stable performance even when the sample size is small. We prove that our estimators satisfy consistency and asymptotic normality. We also provide a consistent estimator for the asymptotic variance. We show via extensive simulations that our proposed method dominates existing alternatives.