Functional Regression with Functional Response by Signal Compression

• Activity Number: 434
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Ruiyan Luo* and Xin Qi
• Companies: Georgia State University and Georgia State University
• Keywords: functional regression model ; functional response ; signal compression ; functional principal component

Abstract

We consider the functional regression model in which both predictor and response are functions. The response function is the sum of a signal function and a random noise function, where the former is the integral of the product of a bi-variate coefficient function and the predictor function. Several double basis expansions have been proposed to approximate the coefficient function, including B-spline basis and the basis obtained from principal component analysis for the predictors. We propose an optimal expansion of the coefficient function in the sense that for any k, the integral of the product of the truncated expansion containing only the first k terms and the predictor curve is the best k-dimensional approximation to the signal function in response. Therefore, through the expansion, the signal is compressed in the first few terms in the expansion as much as possible. To estimate the terms in the expansion, we propose to solve a generalized functional eigenvalue problem, whose eigenvalues indicate the relative importance of the corresponding terms. We provide asymptotic results for the estimation. Simulation studies show the proposed method is competitive in prediction.