Inference on the primary parameter of interest with the aid of dimension reduction estimation

As high dimensional data become routinely available in applied sciences, sufficient dimension reduction has been widely employed and its research has received considerable attention. However, with the majority of sufficient dimension reduction methodology focusing on the dimension reduction step, complete analysis and inference after dimension reduction have yet to receive much attention. We couple the strategy of sufficient dimension reduction with a flexible semiparametric model. We concentrate on inference with respect to the primary variables of interest, and we employ sufficient dimension reduction to bring down the dimension of the regression effectively. Extensive simulations demonstrate the efficacy of the method proposed, and a real data analysis is presented for illustration.