Estimation of parameters of regularly varying distributions on convex cones

TL;DR

This paper extends parameter estimation methods for stable distributions to regularly varying tail distributions on convex cones, proving consistency and asymptotic normality, and optimizing convergence through a modified sampling method.

Contribution

It introduces a new estimation approach for regularly varying distributions on convex cones, with proven statistical properties and improved convergence rates.

Findings

Establishes consistency and asymptotic normality of estimators.

Proposes a modified sampling method for better convergence.

Extends estimation techniques to distributions on convex cones.

Abstract

The objective of this paper is to extend an estimation method of parameters of the stable distributions in $\rd$ to the regularly varying tails distributions in an arbitrary cone. The consistency and the asymptotic normality of estimators are proved. The sampling method of regrouping is modified to optimize the rate of convergence of estimators.