SVD-Bootstrap for Detection of Tensor Changes

Barbora Peštová (), Michal Pešta () and Martin Romaňák ()
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Barbora Peštová: Charles University, Department of Probability and Mathematical Statistics, Faculty of Mathematics and Physics
Michal Pešta: Charles University, Department of Probability and Mathematical Statistics, Faculty of Mathematics and Physics
Martin Romaňák: Charles University, Department of Probability and Mathematical Statistics, Faculty of Mathematics and Physics

Chapter Chapter 9 in Asymptotic and Methodological Statistics, 2026, pp 173-196 from Springer

Abstract: Abstract Multivariate observations over the items and across the subjects with longitudinal and cross-sectional dependence naturally form a stochastic tensor data structure. Several types of changes in tensor means are considered. A class of changepoint detection methods is investigated. These procedures do not require training data and, moreover, are completely distribution-free and tuning-parameter-free. We propose SVD-bootstrap superstructure that overcomes the computational curse of dimensionality without any loss of information. The empirical properties of the detection technique are investigated through a simulation study. The fully data-driven test is applied to real-world data from EEG.

Date: 2026
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DOI: 10.1007/978-3-032-07178-1_9

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