Statistics and Its Interface
Volume 12 (2019)
A martingale-difference-divergence-based estimation of central mean subspace
Pages: 489 – 500
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.
central mean subspace, distance covariance, martingale difference divergence, multiple index models, sufficient dimension reduction
Research for this article was supported in part by the National Natural Science Foundation of China (11426156, 11501372).
Received 6 October 2018
Published 4 June 2019