Pearson Coefficient Degradation in a Wasserstein/Gelbrich Ambiguity Set - Archive ouverte HAL
Article Dans Une Revue IEEE Control Systems Letters Année : 2024

Pearson Coefficient Degradation in a Wasserstein/Gelbrich Ambiguity Set

Résumé

This paper presents new results on the Gelbrich distance and the corresponding ambiguity sets, to analyze the correlation between two scalar random variables. A closed expression of the minimum disturbance in the Gelbrich metric necessary to achieve a specified correlation between two random variables is proposed. This expression allows us to analytically compute the minimal absolute correlation in a Gelbrich ball. This analysis facilitates the assessment of the robustness of the Pearson coefficient within an ambiguity set. Two numerical examples illustrate the validity of the proposed results
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Dates et versions

hal-04607918 , version 1 (11-06-2024)

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Citer

Matthieu Borelle, Teodoro Alamo, Cristina Stoica, Sylvain Bertrand, Eduardo Camacho. Pearson Coefficient Degradation in a Wasserstein/Gelbrich Ambiguity Set. IEEE Control Systems Letters, 2024, 8, pp.1331-1336. ⟨10.1109/LCSYS.2024.3410639⟩. ⟨hal-04607918⟩
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