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November 2019 Principal components analysis of regularly varying functions
Piotr Kokoszka, Stilian Stoev, Qian Xiong
Bernoulli 25(4B): 3864-3882 (November 2019). DOI: 10.3150/19-BEJ1113

Abstract

The paper is concerned with asymptotic properties of the principal components analysis of functional data. The currently available results assume the existence of the fourth moment. We develop analogous results in a setting which does not require this assumption. Instead, we assume that the observed functions are regularly varying. We derive the asymptotic distribution of the sample covariance operator and of the sample functional principal components. We obtain a number of results on the convergence of moments and almost sure convergence. We apply the new theory to establish the consistency of the regression operator in a functional linear model.

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Piotr Kokoszka. Stilian Stoev. Qian Xiong. "Principal components analysis of regularly varying functions." Bernoulli 25 (4B) 3864 - 3882, November 2019. https://doi.org/10.3150/19-BEJ1113

Information

Received: 1 June 2018; Revised: 1 December 2018; Published: November 2019
First available in Project Euclid: 25 September 2019

zbMATH: 07110158
MathSciNet: MR4010975
Digital Object Identifier: 10.3150/19-BEJ1113

Keywords: functional data , principal components , regular variation

Rights: Copyright © 2019 Bernoulli Society for Mathematical Statistics and Probability

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Vol.25 • No. 4B • November 2019
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