Calibration Estimation of Semiparametric Copula Models with Data Missing at Random

This paper investigates the estimation of semiparametric copula models with data missing at random. The two-step maximum likelihood estimation of Genest, Ghoudi, and Rivest (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 missing mechanism, and enjoy stable performance even when 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