Article Dans Une Revue Electronic Journal of Statistics Année : 2025

Correlation tests and sample spectral coherence matrix in the high-dimensional regime

Résumé

It is established that the linear spectral statistics (LSS) of the smoothed periodogram estimate of the spectral coherence matrix of a complex Gaussian high-dimensional times series (yn) n∈Z with independent components satisfy at each frequency a central limit theorem in the asymptotic regime where the sample size N , the dimension M of the observation, and the smoothing span B both converge towards +∞ in such a way that M = O(N α ) for α < 1 and M B → c, c ∈ (0, 1). It is deduced that two recentered and renormalized versions of the LSS, one based on an average in the frequency domain and the other one based on a sum of squares also in the frequency domain, and both evaluated over a well-chosen frequency grid, also verify a central limit theorem. These two statistics are proposed to test with controlled asymptotic level the hypothesis that the components of y are independent. Numerical simulations assess the performance of the two tests.

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Dates et versions

hal-04856829 , version 1 (07-01-2025)
hal-04856829 , version 2 (17-11-2025)

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Philippe Loubaton, Alexis Rosuel, Pascal Vallet. Correlation tests and sample spectral coherence matrix in the high-dimensional regime. Electronic Journal of Statistics , 2025, 19 (2), pp.5577-5694. ⟨10.1214/25-EJS2467⟩. ⟨hal-04856829v2⟩
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