Statistics and Its Interface

Volume 12 (2019)

Number 3

A martingale-difference-divergence-based estimation of central mean subspace

Pages: 489 – 500

DOI: https://dx.doi.org/10.4310/19-SII562

Authors

Yu Zhang (School of Mathematical Sciences,, Peking University, Beijing, China)

Jicai Liu (College of Mathematics and Sciences, Shanghai Normal University, Shanghai, China)

Yuesong Wu (College of Mathematics and Sciences, Shanghai Normal University, Shanghai, China)

Xiangzhong Fang (School of Mathematical Sciences,, Peking University, Beijing, China)

Abstract

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.

Keywords

central mean subspace, distance covariance, martingale difference divergence, multiple index models, sufficient dimension reduction

Full Text (PDF format)

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