Common functional principal components
| Autor: | Alois Kneip, Wolfgang Karl Härdle, Michal Benko |
|---|---|
| Rok vydání: | 2009 |
| Předmět: |
Statistics and Probability
Two Sample Problem 17 Wirtschaft Inference Mathematics - Statistics Theory Sample (statistics) Statistics Theory (math.ST) 62H25 62G08 (Primary) 62P05 (Secondary) Implied volatility Functional Principal Components Nonparametric Regression Bootstrap Two Sample Problem 62P05 Functional principal components 62G08 Nonparametric Regression ddc:330 FOS: Mathematics Decomposition (computer science) two sample problem 62H25 Applied mathematics bootstrap Eigenvalues and eigenvectors Mathematics Functional principal component analysis 330 Wirtschaft Eigenfunction Bootstrap jel:C14 nonparametric regression Principal component analysis jel:G19 Functional Principal Components Statistics Probability and Uncertainty |
| Zdroj: | Ann. Statist. 37, no. 1 (2009), 1-34 |
| ISSN: | 0090-5364 |
| Popis: | Functional principal component analysis (FPCA) based on the Karhunen--Lo\`{e}ve 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. Comment: Published in at http://dx.doi.org/10.1214/07-AOS516 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org) |
| Databáze: | OpenAIRE |
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