Estimation of sub-Gaussian random vectors using the method of moments

TL;DR

This paper introduces a method for estimating sub-Gaussian stable distributions using the method of moments applied to the empirical characteristic function, with proven convergence, limiting distribution, and finite-sample performance.

Contribution

It proposes a novel estimation technique for sub-Gaussian stable distributions based on the method of moments and empirical characteristic functions.

Findings

Estimators converge almost surely.

Derived the limiting distribution of estimators.

Demonstrated good finite-sample performance.

Abstract

The sub-Gaussian stable distribution is a heavy-tailed elliptically contoured law which has interesting applications in signal processing and financial mathematics. This work addresses the problem of feasible estimation of distributions. We present a method based on 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.