Testing the Equality of Covariance Operators in Functional Samples

By Stefan Fremdt, Josef G. Steinebach, Lajos Horv'ath, Piotr Kokoszka. 2011

101 citations recorded by the source corpus.

Abstract. We propose a non‐parametric test for the equality of the covariance structures in two functional samples. The test statistic has a chi‐square asymptotic distribution with a known number of degrees of freedom, which depends on the level of dimension reduction needed to represent the data. Detailed analysis of the asymptotic properties is developed. Finite sample perfo‐rmance is examined by a simulation study and an application to egg‐laying curves of fruit flies.

Subfields: Global and Planetary Change, Nature and Landscape Conservation, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/8a0e765c9f31c734a69961638dd652430e630ce0

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In Global and Planetary Change

In Nature and Landscape Conservation

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Citations in the corpus

Bootstrap-based testing of equality of mean functions or equality of covariance operators for functional data (2016, methodology): “This has motivated many researchers to consider test statistics that are based on finite-dimensional projections, leading to more tractable asymptotic distributions; see Horváth & Kokoszka (2012, Ch. 5), Panaretos et al. (2010) and Fremdt et al. (2012).”
A Two Sample Distribution-Free Test for Functional Data with Application to a Diffusion Tensor Imaging Study of Multiple Sclerosis (2016, methodology): “For detecting differences in the covariance functions of independent samples of curves Ferraty et al. (2007) proposed a factor-based test, Kraus and Panaretos (2012) introduced a regularized M-test and Fremdt et al. (2012) proposed a χ2test.”
Testing relevant hypotheses in functional time series via self‐normalization (2018, background): “09) compare linear operators in two functional regression models, Benko et al. (2009) propose functional principal component analysis (FPCA) for two sample inference while Panaretos et al. (2010) and Fremdt et al. (2013) consider a test for the equality of covariance operators. More recently Horvath”
Fourier analysis of stationary time series in function space (2013, background): “…with respect to their covariance structure [e.g., Panaretos, Kraus and Maddocks (2010), Boente, Rodriguez and Sued (2011), Horváth and Kokoszka (2012), Fremdt et al. (2013)], and in the context of detection of sequential changes in the covariance structure of functional observations [Horváth,…”
Distances and inference for covariance operators (2014, methodology): “Some recent work (Panaretos et al., 2010; Fremdt et al., 2013) has examined testing the equality of covariance structures from two groups of functional curves by defining a test statistic through the Karhunen–Loève expansions of the two covariance structures.”
Uniform change point tests in high dimension (2015, result): “[6, 26, 30]), the literature in the latter case is rather sparse compared to the univariate theory.”