A note on the Lindeberg condition for convergence to stable laws in Mallows distance

TL;DR

This paper corrects and improves a condition for convergence to stable laws in Mallows distance, framing it as a Lindeberg-like condition to enhance understanding and applicability.

Contribution

It rectifies a previous result and provides an improved, more familiar Lindeberg-like condition for convergence to stable laws in Mallows distance.

Findings

Corrects a condition in Johnson and Samworth's result

Provides an improved, more accessible convergence condition

Frames the result in a Lindeberg-like context

Abstract

We correct a condition in a result of Johnson and Samworth (Bernoulli 11 (2005) 829--845) concerning convergence to stable laws in Mallows distance. We also give an improved version of this result, setting it in the more familiar context of a Lindeberg-like condition.