On Linear Estimators for some Stable Vectors

Rayan Chouity; Charbel Hannoun; Jihad Fahs; Ibrahim Abou-Faycal

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arXiv · 2601.09554

On Linear Estimators for some Stable Vectors

Rayan Chouity·Charbel Hannoun·Jihad Fahs·Ibrahim Abou-Faycal

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Abstract

We consider the estimation problem for jointly stable random variables. Under two specific dependency models: a linear transformation of two independent stable variables and a sub-Gaussian symmetric $\alpha$-stable (S$\alpha$S) vector, we show that the conditional mean estimator is linear in both cases. Moreover, we find dispersion optimal linear estimators. Interestingly, for the sub-Gaussian (S$\alpha$S) vector, both estimators are identical generalizing the well-known Gaussian result of the conditional mean being the best linear minimum-mean square estimator.

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Rayan Chouity, Charbel Hannoun, Jihad Fahs, Ibrahim Abou-Faycal. 2026-01-14. On Linear Estimators for some Stable Vectors. https://arxiv.org/abs/2601.09554

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