Estimation of the multivariate symmetric stable distribution using the method of moments

Taras Bodnar, Dmitry Otryakhin and Erik Thorsén

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 16, 5039-5056

Abstract: The multivariate symmetric stable distribution is a heavy-tailed elliptically contoured law that has many important applications in signal processing and financial mathematics. The family includes the sub-Gaussian stable distribution as a special case. This work addresses the problem of feasible estimation of the parameters of the multivariate symmetric stable distribution. We present a method based on the application of the method of moments to the empirical characteristic function. Further, we show almost sure convergence of our estimators, discover their limiting distribution, and demonstrate their finite-sample performance.

Date: 2025
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DOI: 10.1080/03610926.2024.2430746

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