Trimmed L-moments For Estimation Multi-parameter Archimedean Copulas

TL;DR

This paper introduces a new estimation method for multi-parameter Archimedean copulas using trimmed L-moments, addressing challenges with heavy-tailed distributions where traditional L-moments are invalid.

Contribution

It proposes a novel estimation approach based on trimmed L-moments for copulas, with proven consistency and asymptotic normality, supported by simulation studies.

Findings

The new estimator is consistent and asymptotically normal.

Simulation results demonstrate the effectiveness of the proposed method.

The method extends L-moments applicability to heavy-tailed distributions.

Abstract

Trimmed L-moments, were introduced by Elamir and Seheult(2003) to proposed a new estimation method for multi-parameter distributions when the mean doesn't exist or for heavy tailed distribution where the L-moments method which proposed by Hosking (1990) is not valid because the absence of theoretical L-moments. In this paper a new estimation method based on trimmed L-moments of multi-parameter copulas is proposed with a simulation study. The consistency and the asymptotic normality of the new estimator also established.