Copula-based Partial Correlation Screening: a Joint and Robust Approach

Abstract: Screening for ultrahigh dimensional features may encounter complicated issues such as outlying observations, heteroscedasticity or heavy-tailed distribution, multi-collinearity and confounding effects. Standard correlation-based marginal screening methods may be a weak solution to these issues. We contribute a novel robust joint screener to safeguard against outliers and distribution mis-specification for both the response variable and the covariates, and to account for external variables at the screening step. Specifically, we introduce a copula-based partial correlation (CPC) screener. We show that the empirical process of the estimated CPC converges weakly to a Gaussian process and establish the sure screening property for CPC screener under very mild technical conditions, where we need not require any moment condition, weaker than existing alternatives in the literature. Moreover, our approach allows for a diverging number of conditional variables from the theoretical point of view. Extensive simulation studies and two data applications are included to illustrate our proposal.