摘要：In this article, we propose a new method for estimating the central mean subspace via the martingale difference divergence. This method enjoys a model free property and does not need any nonparametric estimation. These advantages enable our method to work effectively when many discrete or categorical predictors exist. Under mild conditions, we show that our estimator is root-$n$ consistent. To determine the structural dimension of the central mean subspace, a consistent Bayesian-type information criterion is developed. Simulation studies and a real data example are given to illustrate the proposed estimation methodology..
关键词：central mean subspace; distance covariance; martingale difference divergence; multiple index models; sufficient dimension reduction
