On Linear Estimators for some Stable Vectors

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.