A Flexibly Conditional Screening Approach via a Nonparametric Quantile Partial Correlation

Considering the influence of conditional variables is crucial to statistical modeling, ignoring this may lead misleading results. Recently, Ma, Li and Tsai proposed quantile partial correlation (QPC)-based screening approach that takes into account for ultrahigh dimensional data. In paper, we propose a nonparametric version (NQPC), which able describe on other relevant more flexibly precisely. Specifically, NQPC firstly removes effect via fitting two additive models, differs from conventional fits parametric secondly computes QPC resulting residuals as NQPC. This measure very useful in situation where are highly nonlinearly correlated with both predictors response. Then, employ utility do variable screening. A procedure based NPQC (NQPC-SIS) proposed. Theoretically, prove NQPC-SIS enjoys sure property that, probability going one, selected subset can recruit all truly important under mild conditions. Finally, extensive simulations an empirical application carried out demonstrate usefulness our proposal.