期刊
JOURNAL OF MULTIVARIATE ANALYSIS
卷 146, 期 -, 页码 301-312出版社
ELSEVIER INC
DOI: 10.1016/j.jmva.2015.10.003
关键词
Functional prediction; Functional principal component analysis; Functional regression; Multivariate functional data; Stochastic processes
资金
- Academia Sinica [M037]
- Ministry of Science and Technology, Taiwan [NSC 101-2118-M-001-MY3]
We propose a multivariate functional linear regression (mFLR) approach to analysis and prediction of multivariate functional data in cases in which, both the response and predictor variables contain multivariate random functions. The mFLR model, coupled with the multivariate functional principal component analysis approach, takes the advantage of cross-correlation between component functions within the multivariate response and predictor variables, respectively. The estimate of the matrix of bivariate regression functions is consistent in the sense of the multi-dimensional Gram-Schmidt norm and is asymptotically normally distributed. The prediction intervals of the multivariate random trajectories are available for predictive inference. We show the finite sample performance of mFLR by a simulation study and illustrate the method through predicting multivariate traffic flow trajectories for up-to-date and partially observed traffic streams. (C) 2015 Elsevier Inc. All rights reserved.
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