Bootstrapping the Mean Vector for the Observations in the Domain of Attraction of a Multivariate Stable Law

TL;DR

This paper introduces a robust bootstrap method for estimating the mean vector of multivariate heavy-tailed distributions within the domain of attraction of stable laws, providing asymptotic Gaussianity and valid confidence regions.

Contribution

It proposes a novel bootstrap-based estimator for the mean vector in multivariate stable law domains, demonstrating its efficiency through simulations.

Findings

Estimator is asymptotically Gaussian with unknown parameters.

Bootstrap confidence regions are valid for heavy-tailed data.

Simulation confirms the method's efficiency in inference.

Abstract

We consider a robust estimation of the mean vector for a sequence of i.i.d. observations in the domain of attraction of a stable law with different indices of stability, $DS(\alpha_1, \ldots, \alpha_p)$, such that $1<\alpha_{i}\leq 2$, $i=1,\ldots,p$. The suggested estimator is asymptotically Gaussian with unknown parameters. We apply an asymptotically valid bootstrap to construct a confidence region for the mean vector. A simulation study is performed to show that the estimation method is efficient for conducting inference about the mean vector for multivariate heavy-tailed distributions.