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For instance, if j = u and (j − k)(j − v)(k − v) ̸= 0, E[(z⊤ 1jz1k)(z⊤ 1uz1v)] = E[(a⊤b)(a⊤c)] = E   p1X i1,i2=1 ai1bi1ai2ci2   = nX i1,i2=1 E [ai1ai2] E[bi1]E[ci2] = 0

Otherwise, using the independence of entries of a, b, c, d yields that E[(z⊤ 1jz1k)(z⊤ 1uz1v)] = 0

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Testing Separability of High-Dimensional Covariance Matrices

math.ST · 2025-06-20 · unverdicted · novelty 7.0

Proposes invariant tests for separability of high-dimensional covariance matrices by showing equivalence to sphericity testing on the core component, with asymptotic spectral equivalence results and numerical power comparisons.

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  • Testing Separability of High-Dimensional Covariance Matrices math.ST · 2025-06-20 · unverdicted · none · ref 62

    Proposes invariant tests for separability of high-dimensional covariance matrices by showing equivalence to sphericity testing on the core component, with asymptotic spectral equivalence results and numerical power comparisons.