  In this paper, we propose two new methods to estimate the dimension-reduction
directions of the central subspace (CS) by constructing a regression model such
that the directions are all captured in the regression mean. Compared with the
inverse regression estimation methods (e.g. Li, 1991, 1992; Cook and Weisberg,
1991), the new methods require no strong assumptions on the design of
covariates or the functional relation between regressors and the response
variable, and have better performance than the inverse regression estimation
methods for finite samples. Compared with the direct regression estimation
methods (e.g. H\"ardle and Stoker, 1989; Hristache, Juditski, Polzehl and
Spokoiny, 2001; Xia, Tong, Li and Zhu, 2002), which can only estimate the
directions of CS in the regression mean, the new methods can detect the
directions of CS exhaustively. Consistency of the estimators and the
convergence of corresponding algorithms are proved.
