Estimation of the spectral measure of multivariate regularly varying distributions

TL;DR

This paper extends an estimator for the spectral measure from multivariate stable to regularly varying distributions, optimizing convergence and proposing a total mass estimator with proven consistency and asymptotic normality.

Contribution

It introduces an improved estimator for the spectral measure of multivariate regularly varying distributions and proves its statistical properties.

Findings

Estimator for spectral measure extended and optimized.

Proposed estimator for total mass of spectral measure.

Proved consistency and asymptotic normality.

Abstract

In the paper, the estimator for the spectral measure of multivariate stable distributions introduced by Davydov and co-workers are extended to the regularly varying distributions. The sampling method is modified to optimize the rate of convergence of estimator. An estimator of the total mass of spectral measure is proposed. The consistency and the asymptotic normality of estimators are proved.