Estimation and inference on central mean subspace for multivariate response data

In this paper, we introduce the notion of the central mean subspace when the response is multivariate, and propose a profile least squares approach to perform estimation and inference. Unlike existing methods in the sufficient dimension reduction literature, the profile least squares method does not require any distributional assumptions on the covariates, and facilitates statistical inference on the central mean subspace. We demonstrate theoretically and empirically that the properly weighted profile least squares approach is more efficient than its unweighted counterpart. We further confirm the promising finite-sample performance of our proposal through comprehensive simulations and an application to an etiologic study on essential hypertension conducted in P. R. China.