Functional linear regression for functional response via sparse basis selection

• Published in: Journal of the Korean Statistical Society Vol. 44; no. 3; pp. 376 - 389
• Main Authors: Han, Kyunghee, Shin, Hyejin
• Format: Journal Article
• Language: English
• Published: Singapore Elsevier B.V 01.09.2015; Springer Singapore; 한국통계학회
• Subjects: Applied Statistics; Basis selection; Bayesian Inference; Functional linear regression; Functional response; Group variable selection; Oracle property; Penalized least squares; Statistical Theory and Methods; Statistics; Statistics and Computing/Statistics Programs; 통계학; secondary; Functional response; Functional linear regression; Oracle property; Basis selection; Penalized least squares; primary; Group variable selection; primary 62J07; secondary 62H12
• ISSN: 1226-3192; 2005-2863
• DOI: 10.1016/j.jkss.2014.10.004

We study a sparse estimation in functional linear regression model for functional response where the bivariate regression coefficient function takes zero values in a certain region of domain, so it is generated by a sparse set of basis functions. From a variable selection perspective, we construct a sparse basis representation for the coefficient function using the penalized least squares method. The proposed method enables us to simultaneously estimate the regression parameters and select basis functions. For a given basis, we show that our approach consistently identifies true subset of basis functions and the resulting estimator has asymptotically the same properties as the oracle estimator derived from the true underlying model. Simulation studies and a real data application are provided to demonstrate a finite sample performance of the proposed method.