Data driven extreme value distribution estimation: Derivation of the Mean Integrated Squared Error, optimal bandwidth selection and stability conditions

TL;DR

This paper presents a kernel-based data-driven estimator for extreme value distributions, deriving its MISE, optimal bandwidth, and stability conditions to improve estimation accuracy.

Contribution

It introduces the DDEVD estimator, providing a detailed MISE derivation, bandwidth selection method, and stability analysis, advancing non-parametric extreme value estimation.

Findings

Derived the MISE for the DDEVD estimator

Proposed an optimal bandwidth selection method

Established stability conditions for the estimator

Abstract

We introduce the data driven extreme value distribution (DDEVD) estimator, a kernel-based method for estimating extreme value distributions from data. We derive its mean integrated squared error (MISE) in detail, use it to compute the optimal bandwidth and establish stability conditions for the bandwidth optimization procedure.