Efficient dimension reduction for multivariate response data

We propose a semiparametric approach to reduce the covariate dimension for multivariate response data. The method bypasses the conventional inverse regression procedure hence seamlessly avoids the potential difficulties related to the dimension of the response. In addition, coupled with a proper parameterization, the approach allows for statistical inference of the dimension reduction subspace for a wide range of models. The resultant estimator is shown to be root-n consistent, asymptotically normal and semiparametrically efficient. The efficiency gain of the semiparametric approach is significant in both simulations and an application to a primary hypertension study conducted in PR China.