Statistics and Its Interface

Volume 6 (2013)

Number 2

Dimension reduction in functional regression using mixed data canonical correlation analysis

Pages: 187 – 196

DOI: https://dx.doi.org/10.4310/SII.2013.v6.n2.a3

Authors

Nan Lin (Department of Mathematics, Washington University in St. Louis, Missouri, U.S.A.)

Guochang Wang (Key Laboratory for Applied Statistics of MOE and School of Mathematics and Statistics, Northeast Normal University, Changchun, China)

Baoxue Zhang (Key Laboratory for Applied Statistics of MOE and School of Mathematics and Statistics, Northeast Normal University, Changchun, China)

Abstract

We propose a new dimension reduction method, mixed data canonical correlation (MDCANCOR), for functional regression with a scalar response and a functional predictor. MDCANCOR achieves dimension reduction using the canonical correlation analysis between the functional predictor and a set of B-spline basis functions that represent the transformed response space. And we propose a modified version of BIC to determine the dimensionality of the effective dimension reduction (EDR) space. This criterion is generally applicable to dimension reduction problems in functional regression. Asymptotically, we prove that MDCANCOR consistently estimates the directions when the dimensionality of the EDR space is given, and the modified BIC consistently estimates the dimensionality of the EDR space. Both simulation and real data examples show that the MDCANCOR method performs similarly as the regularized functional sliced inverse regression and better than other existing dimension reduction methods.

Keywords

dimension reduction, effective dimension reduction, functional regression, mixed-data canonical correlation, splines

2010 Mathematics Subject Classification

Primary 62G05, 62G08. Secondary 62G20.

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Published 10 May 2013