Faster convergence rate for functional linear regression in reproducing kernel Hilbert spaces. Issue 1 (2nd January 2020)

• Record Type: Journal Article
• Authors: Zhang, Fode; Zhang, Weiping; Li, Rui; Lian, Heng
• Is Part Of: Statistics. Volume 54:Issue 1(2020)
• Page Start: 167
• Page End: 181
• Publication Date: 2020-01-02
• Subjects: Convergence rate -- functional data -- reproducing kernel Hilbert space; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2019.1694931
• Languages: English
• ISSNs: 0233-1888

Abstract

ABSTRACT: Functional linear regression is in the centre of research attention involving curves as units of observations. We focus on functional linear regression in the framework of reproducing kernel Hilbert spaces studied in Cai and Yuan [Minimax and adaptive prediction for functional linear regression. J Am Stat Assoc. 2012;107(499):1201–1216]. We extend their theoretical result establishing faster convergence rate under stronger conditions which is reduced to existing results when the stronger condition is removed. In particular, our result corroborates the expectation that with smoother functions the convergence rate of the estimator is faster.