Directional regression is an effective sufficient dimension reduction method which implicitly synthesizes the first two conditional moments. In this paper, we extend directional regression to a general family of estimators via the notion of general empirical directions. Data-driven method is...

Sufficient dimension reduction aims at finding transformations of predictor X without losing any regression information of Y versus X. If we are only interested in the information contained in the mean function or the kth moment function of Y given X, estimation of the central mean space or the...

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...

Classical sufficient dimension reduction methods are sensitive to outliers present in predictors, and may not perform well when the distribution of the predictors is heavy-tailed. In this paper, we propose two robust inverse regression methods which are insensitive to data contamination:...

We propose a link-free procedure for testing whether two multi-index models share identical indices via the sufficient dimension reduction approach. Test statistics are developed based upon three different sufficient dimension reduction methods: (i) sliced inverse regression, (ii) sliced average...