Moment Estimator-Based Extreme Quantile Estimation with Erroneous Observations: Application to Elliptical Extreme Quantile Region Estimation

TL;DR

This paper investigates how measurement errors affect moment-based extreme quantile estimation across various distribution types and proposes conditions where errors become negligible, with applications to elliptical distribution regions.

Contribution

It provides a theoretical analysis of error impacts on extreme value estimation and introduces conditions for asymptotic negligibility, with practical application to elliptical distributions.

Findings

Errors can be asymptotically negligible under certain conditions.

The analysis covers all types of tail distributions.

Application to multivariate elliptical distributions demonstrates practical relevance.

Abstract

In many application areas of extreme value theory, the variables of interest are not directly observable but instead contain errors. In this article, we quantify the effect of these errors in moment-based extreme value index estimation, and in corresponding extreme quantile estimation. We consider all, short-, light-, and heavy-tailed distributions. In particular, we derive conditions under which the error is asymptotically negligible. As an application, we consider affine equivariant extreme quantile region estimation under multivariate elliptical distributions.