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2018 Principal quantile regression for sufficient dimension reduction with heteroscedasticity
Chong Wang, Seung Jun Shin, Yichao Wu
Electron. J. Statist. 12(2): 2114-2140 (2018). DOI: 10.1214/18-EJS1432

Abstract

Sufficient dimension reduction (SDR) is a successful tool for reducing data dimensionality without stringent model assumptions. In practice, data often display heteroscedasticity which is of scientific importance in general but frequently overlooked since a primal goal of most existing statistical methods is to identify conditional mean relationship among variables. In this article, we propose a new SDR method called principal quantile regression (PQR) that efficiently tackles heteroscedasticity. PQR can naturally be extended to a nonlinear version via kernel trick. Asymptotic properties are established and an efficient solution path-based algorithm is provided. Numerical examples based on both simulated and real data demonstrate the PQR’s advantageous performance over existing SDR methods. PQR still performs very competitively even for the case without heteroscedasticity.

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Chong Wang. Seung Jun Shin. Yichao Wu. "Principal quantile regression for sufficient dimension reduction with heteroscedasticity." Electron. J. Statist. 12 (2) 2114 - 2140, 2018. https://doi.org/10.1214/18-EJS1432

Information

Received: 1 March 2017; Published: 2018
First available in Project Euclid: 13 July 2018

zbMATH: 1393.60119
MathSciNet: MR3827816
Digital Object Identifier: 10.1214/18-EJS1432

Subjects:
Primary: 60K35

Keywords: Heteroscedasticity , kernel quantile regression , principal quantile regression , sufficient dimension reduction

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Vol.12 • No. 2 • 2018
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