Dimension reduction in semiparametric regressions includes construction of informative linear combinations and selection of contributing predictors. To reduce the predictor dimension in semiparametric regressions, we propose an ℓ₁-minimization of sliced inverse regression with the Dantzig...

Partial dimension reduction is a general method to seek informative convex combinations of predictors of primary interest, which includes dimension reduction as its special case when the predictors in the remaining part are constants. In this article, we propose a novel method to conduct partial...

Existing model-free tests of the conditional coordinate hypothesis in sufficient dimension reduction (Cook (1998) [3]) focused mainly on the first-order estimation methods such as the sliced inverse regression estimation (Li (1991) [14]). Such testing procedures based on quadratic inference...