Model-free coordinate test and variable selection via directional regression

We consider the paradigm of marginal coordinate tests (Cook (2004)) for model-free variable selection. To combine the strength of existing tests based on sliced inverse regression and sliced average variance estimation, we design a new marginal coordinate test via directional regression. Given the method-specific marginal coordinate test statistics, a maximum ratio criteria is proposed to facilitate model-free variable selection. Under mild conditions, the variable-selection consistency is guaranteed when n goes to ∞.