Minimax prediction for functional linear regression with functional responses in reproducing kernel Hilbert spaces

JOURNAL OF MULTIVARIATE ANALYSIS

卷:140

Article

Lian, Heng

关键词: Functional data;    Functional response;    Minimax convergence rate;    Regularization;   

DOI  :  10.1016/j.jmva.2015.06.005

来源: Elsevier

【 摘 要 】

In this article, we consider convergence rates in functional linear regression with functional responses, where the linear coefficient lies in a reproducing kernel Hilbert space (RKHS). Without assuming that the reproducing kernel and the covariate covariance kernel are aligned, convergence rates in prediction risk are established. The corresponding lower bound in rates is derived by reducing to the scalar response case. Simulation studies and two benchmark datasets are used to illustrate that the proposed approach can significantly outperform the functional PCA approach in prediction. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free