The Annals of Statistics
- Ann. Statist.
- Volume 37, Number 1 (2009), 1-34.
Common functional principal components
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.
Ann. Statist. Volume 37, Number 1 (2009), 1-34.
First available in Project Euclid: 16 January 2009
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62H25: Factor analysis and principal components; correspondence analysis 62G08: Nonparametric regression
Secondary: 62P05: Applications to actuarial sciences and financial mathematics
Benko, Michal; Härdle, Wolfgang; Kneip, Alois. Common functional principal components. Ann. Statist. 37 (2009), no. 1, 1--34. doi:10.1214/07-AOS516. https://projecteuclid.org/euclid.aos/1232115926.