Nonparametric two sample test of spectral densities

Ilaria Nadin; Tatyana Krivobokova; Farida Enikeeva

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arXiv · 2602.10774

Nonparametric two sample test of spectral densities

Ilaria Nadin·Tatyana Krivobokova·Farida Enikeeva

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Abstract

A novel nonparametric test for the equality of the covariance matrices of two Gaussian stationary processes, possibly of different lengths, is proposed. The test translates to testing the equality of two spectral densities and is shown to be minimax rate-optimal. Test performance is validated in a simulation study, and the practical utility is demonstrated in the analysis of real electroencephalography data. The test is implemented in the R-package sdf.test.

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Ilaria Nadin, Tatyana Krivobokova, Farida Enikeeva. 2026-02-11. Nonparametric two sample test of spectral densities. https://arxiv.org/abs/2602.10774

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