Nonparametric two sample test of spectral densities

TL;DR

This paper introduces a new nonparametric spectral density equality test for Gaussian stationary processes, demonstrating its optimality, practical utility in EEG data analysis, and providing an R package implementation.

Contribution

It proposes a minimax rate-optimal nonparametric test for spectral density equality, applicable to processes of different lengths, with validation through simulations and real data.

Findings

Test is minimax rate-optimal.

Effective in EEG data analysis.

Available as R package sdf.test.

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.