Copula-Based Regression Models with Responses Missing at Random: A Unified Approach

Abstract

The existing literature of copula-based regression assumes that complete data are available, but this assumption is violated in many real applications. The present paper allows the regressand and regressors to be missing at random (MAR). We formulate a generalized regression model which unifies many prominent cases such as the conditional mean and quantile regressions. A semiparametric copula and the target regression curve are estimated via the calibration approach. The consistency and asymptotic normality of the estimated regression curve are proved. We show via Monte Carlo simulations that the proposed approach operates well in finite samples, while a benchmark equal-weight approach fails with substantial bias under MAR. An empirical application on revenues and R\&D expenses of German manufacturing firms highlights a practical use of our approach.