A moving window approach for nonparametric estimation of the conditional tail index

TL;DR

This paper introduces a nonparametric moving window method for estimating the conditional tail index of Pareto-type distributions, leveraging covariate information to improve tail risk assessment.

Contribution

It proposes a novel moving window estimator that combines weighted log-spacings and a random threshold, with proven asymptotic normality and demonstrated finite sample effectiveness.

Findings

Estimator achieves asymptotic normality under mild conditions

Finite sample performance is validated on real data

Method effectively incorporates covariate information

Abstract

We present a nonparametric family of estimators for the tail index of a Pareto-type distribution when covariate information is available. Our estimators are based on a weighted sum of the log-spacings between some selected observations. This selection is achieved through a moving window approach on the covariate domain and a random threshold on the variable of interest. Asymptotic normality is proved under mild regularity conditions and illustrated for some weight functions. Finite sample performances are presented on a real data study.