Dispersion operators and resistant second-order functional data analysis

By David Kraus, Victor M. Panaretos. 2012

70 citations recorded by the source corpus.

Inferences related to the second-order properties of functional data, as expressed by covariance structure, can become unreliable when the data are non-Gaussian or contain unusual observations. In the functional setting, it is often difficult to identify atypical observations, as their distinguishing characteristics can be manifold but subtle. In this paper, we introduce the notion of a dispersion operator, investigate its use in probing the second-order structure of functional data, and develop a test for comparing the second-order characteristics of two functional samples that is resistant to atypical observations and departures from normality. The proposed test is a regularized M-test based on a spectrally truncated version of the Hilbert--Schmidt norm of a score operator defined via the dispersion operator. We derive the asymptotic distribution of the test statistic, investigate the behaviour of the test in a simulation study and illustrate the method on a structural biology dataset. Copyright 2012, Oxford University Press.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/2dccddcdb32a40c63e2da14ac9d10f3cfafe930e

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Citations in the corpus

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.”
Functional Data Analysis (2016, methodology): “…and contamination and more generally visual exploration of functional data include exploratory box plots (Hyndman & Shang 2010; Sun & Genton 2011) and robust versions of FPCA (Crambes, Delsol & Laksaci 2008; Gervini 2008; Bali et al. 2011; Kraus & Panaretos 2012; Boente & Salibi´an-Barrera 2014).”
Testing relevant hypotheses in functional time series via self‐normalization (2018, unknown): “11), which are similar to those used in Kraus and Panaretos (2012) and in Paparoditis and Sapatinas (2016).”
Bootstrap-based testing of equality of mean functions or equality of covariance operators for functional data (2016, methodology): “Motivated by Kraus & Panaretos (2012), we generate non-Gaussian curves X1 and X2, via Xi (t) = ∑10 k=1{21/2k−1/2 sin(πkt)Vi,k + k−1/2 cos(2πkt)Wi,k}, t ∈ I, (i = 1, 2), where Vi,k and Wi,k (i = 1, 2; k = 1, 2, . . . , 10) are independent t5-distributed random variables.”