A note on the best attainable rates of convergence for estimates of the shape parameter of regular variation

TL;DR

This paper improves the known lower bound on the rates of convergence for estimating the shape parameter of regular variation, advancing theoretical understanding of estimator efficiency.

Contribution

It provides a tighter lower bound on convergence rates, refining previous results by Hall and Welsh from 1984.

Findings

Improved lower bound on convergence rates

Enhanced theoretical limits for shape parameter estimation

Refinement of previous bounds from 1984

Abstract

Hall and Welsh gave in 1984 the lowest bound so far to rates of convergence for estimates of the shape parameter of regular variation. We show that this bound can be improved.