Open Access
November 2020 Asymptotic properties of penalized splines for functional data
Luo Xiao
Bernoulli 26(4): 2847-2875 (November 2020). DOI: 10.3150/20-BEJ1209


Penalized spline methods are popular for functional data analysis but their asymptotic properties have not been established. We present a theoretic study of the $L_{2}$ and uniform convergence of penalized splines for estimating the mean and covariance functions of functional data under general settings. The established convergence rates for the mean function estimation are mini-max rate optimal and the rates for the covariance function estimation are comparable to those using other smoothing methods.


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Luo Xiao. "Asymptotic properties of penalized splines for functional data." Bernoulli 26 (4) 2847 - 2875, November 2020.


Received: 1 July 2019; Revised: 1 January 2020; Published: November 2020
First available in Project Euclid: 27 August 2020

zbMATH: 07256162
MathSciNet: MR4140531
Digital Object Identifier: 10.3150/20-BEJ1209

Keywords: $L_{2}$ convergence , Functional data analysis , Nonparametric regression , penalized splines , Uniform convergence

Rights: Copyright © 2020 Bernoulli Society for Mathematical Statistics and Probability

Vol.26 • No. 4 • November 2020
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