Additive functional regression in reproducing kernel Hilbert spaces under smoothness condition

Yuzhu Tian, Hongmei Lin (), Heng Lian and Zengyan Fan
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Yuzhu Tian: Henan University of Science and Technology
Hongmei Lin: Shanghai University of International Business and Economics
Heng Lian: City University of Hong Kong
Zengyan Fan: Singapore University of Social Sciences

Metrika: International Journal for Theoretical and Applied Statistics, 2021, vol. 84, issue 3, No 6, 429-442

Abstract: Abstract Additive functional model is one popular semiparametric approach for regression with a functional predictor. Optimal prediction error rate has been demonstrated in the framework of reproducing kernel Hilbert spaces (RKHS), which only depends on the property of the RKHS but not on the smoothness of the function. We extend this previous theoretical result by establishing faster convergence rates under stronger conditions which is reduced to existing results when the stronger condition is removed. In particular, our result shows that with a smoother function the convergence rate of the estimator is faster.

Keywords: Convergence rate; Functional data; Reproducing kernel Hilbert space (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00184-020-00797-9

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