Open Access
February 2009 Common functional principal components
Michal Benko, Wolfgang Härdle, Alois Kneip
Ann. Statist. 37(1): 1-34 (February 2009). DOI: 10.1214/07-AOS516


Functional principal component analysis (FPCA) based on the Karhunen–Loève decomposition has been successfully applied in many applications, mainly for one sample problems. In this paper we consider common functional principal components for two sample problems. Our research is motivated not only by the theoretical challenge of this data situation, but also by the actual question of dynamics of implied volatility (IV) functions. For different maturities the log-returns of IVs are samples of (smooth) random functions and the methods proposed here study the similarities of their stochastic behavior. First we present a new method for estimation of functional principal components from discrete noisy data. Next we present the two sample inference for FPCA and develop the two sample theory. We propose bootstrap tests for testing the equality of eigenvalues, eigenfunctions, and mean functions of two functional samples, illustrate the test-properties by simulation study and apply the method to the IV analysis.


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Michal Benko. Wolfgang Härdle. Alois Kneip. "Common functional principal components." Ann. Statist. 37 (1) 1 - 34, February 2009.


Published: February 2009
First available in Project Euclid: 16 January 2009

zbMATH: 1169.62057
MathSciNet: MR2488343
Digital Object Identifier: 10.1214/07-AOS516

Primary: 62G08 , 62H25
Secondary: 62P05

Keywords: bootstrap , functional principal components , Nonparametric regression , two sample problem

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 1 • February 2009
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