We propose a general dimension-reduction method that combines the ideas of likelihood, correlation, inverse regression and information theory. We do not require that the dependence be confined to particular conditional moments, nor do we place restrictions on the predictors or on the regression...

Yin and Cook (J. Roy. Statist. Soc. Ser. B Part 2 64 (2002) 159) recently introduced a new dimension reduction method for regression called Covk. Here, we develop the asymptotic distribution of the Covk test statistic for dimension under weak assumptions. This serves as an analytic counterpart...

We show that the test statistic for dimension in q-based principal Hessian directions (pHd) is distributed as a linear combination of [chi]2 random variables. Simpler distributions can result depending on the distribution of the predictors and the adequacy of the quadratic model.

Yin and Cook [2002. Dimension reduction for the conditional k-th moment in regression. J. Roy. Statist. Soc. B 64, 159-175] established a general equivalence between sliced inverse regression (sir) and a marginal moment method called Covk. In this note, we form a new marginal method called phdk...

In this article, we propose the use of orthogonal series to estimate the inverse mean space. Compared to the original slicing scheme, it significantly improves the estimation accuracy without losing computation efficiency, especially for the heteroscedastic models. Compared to the local...

In this paper we propose a dimension reduction method for estimating the directions in a multiple-index regression based on information extraction. This extends the recent work of Yin and Cook [X. Yin, R.D. Cook, Direction estimation in single-index regression, Biometrika 92 (2005) 371-384] who...

In this article, for the regression mean function of Y on , where Y is a scalar, is a px1 vector and W is a categorical variable, we propose a method, partial sparse MAVE, to achieve sufficient dimension reduction and variable selection on simultaneously. The method relaxes any particular...