Common functional principal components

By M. Benko, Wolfgang Karl Härdle, Alois Kneip. 2009

224 citations recorded by the source corpus.

Functional principal component analysis (FPCA) based on the Karhunen-Lo`eve 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 logreturns of IVs are samples of (smooth) random functions and the methods proposed here study the similarities of their stochastic behavior. Firstly 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 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.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/da25b6a8f023035559e403a04a6aabd2370b8ae5

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Citations in the corpus

Dispersion operators and resistant second-order functional data analysis (2012, methodology): “Aspects of this problem were considered in Benko et al. (2009), who employed a bootstrap procedure to compare subsets of eigenfunctions or eigenvalues of the two samples in a financial context.”
Detecting changes in the mean of functional observations (2009, background): “Returning to the functional setting, a somewhat related problem has recently been studied by Benko et al. (2009), who considered two populations, admitting the PCAs: Xi,p.”
Weakly dependent functional data (2010, background): “Lee [64], Hall and Hosseini-Nasab [33], Reiss and Ogden [51], Benko, Härdle and Kneip [6], Müller and Yao [45]).”
Sequential block bootstrap in a Hilbert space with application to change point analysis (2014, methodology): “The method of functional principal components was used by Kokoszka et al. (2008) in testing for independence in the functional linear model and by Benko, Härdle, & Kneip (2009) in two sample tests for L2[0, 1]-valued random variables, a method that was extended to change point analysis by Berkes et”
Testing the Equality of Covariance Operators in Functional Samples (2011, methodology): “In addition to the work of Benko et al. (2009) and Panaretos et al. (2010), the relevant references are Horváth et al. (2009) and Horváth et al. (2011) who focus, respectively, on the regression kernels in functional linear models and the mean of functional data exhibiting temporal dependence.”
A survey of functional principal component analysis (2014, background): “( 4 ) common FPCA : For a group of functional data samples , Benko et al .”
Functional data analysis for density functions by transformation to a Hilbert space (2016, methodology): “The Karhunen–Loève expansion constitutes the foundation for the commonly used FPCA technique [4, 6, 7, 16, 26, 27, 33].”
Properties of design-based functional principal components analysis (2008, background): “, 1986, Besse and Ramsay, 1986, Cardot, 2000 or Benko et al. 2009) as well as bootstrap properties (Kneip and Utikal, 2001) or sparse data (James et al., 2000). The way data are collected is seldom taken into account in the literature and one generally supposes the data are independent realizations ”
A Two Sample Distribution-Free Test for Functional Data with Application to a Diffusion Tensor Imaging Study of Multiple Sclerosis (2016, methodology): “We test the null hypothesis that the means of various modalities along corresponding tracts is the same for MS patients and controls, using the test that was proposed by Benko et al. (2009) with 5000 bootstrap samples.”
Bootstrap-based testing of equality of mean functions or equality of covariance operators for functional data (2016, methodology): “Benko et al. (2009) and Horváth & Kokoszka (2012, Ch. 5) have developed functional testing procedures for the equality of two or more mean functions.”
Dynamic functional principal components (2012, background): “Statisticians have been working on problems related to estimation and inference (Kneip and Utikal, 2001; Benko et al., 2009), asymptotics (Dauxois et al., 1982; Hall and Hosseini-Nasab, 2006), smoothing techniques (Silverman, 1996), sparse data (James et al., 2000; Hall et al., 2006) and robustness…”
Testing relevant hypotheses in functional time series via self‐normalization (2018, background): “(2009) compared linear operators in two functional regression models and Benko et al. (2009) proposed functional principal component analysis for two-sample inference whereas Panaretos et al. (2010) and Fremdt et al.”
Second-Order Comparison of Gaussian Random Functions and the Geometry of DNA Minicircles (2010, background): “A related recent article by Benko, Härdle, and Kneip (2009) proposed two-sample bootstrap tests for specific aspects of the spectrum of functional data, such as the equality of a subset of the eigenfunctions, or—assuming that the eigenfunctions are shared—equality of a subset of eigenvalues.”