In this paper, new aspects of treatment comparison are brought out via the dimension reduction model of Li (1991) for general regression settings. Denote the treatment indicator by Z and the covariate by X. The model Y = g(v 0 X + Z;) is discussed in detail. Estimates of v and are obtained without assuming a functional form for g. Our method is based on the use of SIR (sliced inverse regression...

Moment-based sufficient dimension reduction methods such as sliced inverse regression may not work well in the presence of heteroscedasticity. We propose to first estimate expectiles through kernel expectile regression, and then carry out based on random projections expectiles. Several popular literature are extended under this general framework. The proposed expectile-assisted outperform exist...

Sliced inverse regression is one of the widely used dimension reduction methods. Chiaromonte and co-workers extended this method to regressions with qualitative predictors and developed a method, partial sliced inverse regression, under the assumption that the covariance matrices of the continuous predictors are constant across the levels of the qualitative predictor. We extend partial sliced i...

We introduce a new sparse sliced inverse regression estimator called Cholesky matrix penalization and its adaptive version for achieving sparsity in estimating the dimensions of central subspace. The estimators use decomposition covariance covariates include regularization term objective function to achieve computationally efficient manner. establish theoretical values tuning parameters that es...