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

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 be a weak solution to these issues. We contribute novel robust joint screener safeguard against outliers distribution mis-specification both the response variable covariates, account external variables at step. Specifically, we introduce copula-based partial correlation (CPC) screener. show that empirical process of estimated CPC converges weakly Gaussian establish sure property under very mild technical conditions, where need not require any moment condition, weaker than existing alternatives in literature. Moreover, our approach allows diverging number conditional from theoretical point view. Extensive simulation studies two data applications are included illustrate proposal.