Robust and Computationally Efficient Trimmed L-Moments Estimation for Parametric Distributions

TL;DR

This paper introduces a robust, efficient method for estimating parameters of distributions using trimmed L-moments, which are less affected by outliers and heavy tails, with proven theoretical properties and practical algorithms.

Contribution

It develops a novel estimation framework based on trimmed L-moments, including algorithms for stable computation and asymptotic analysis, improving robustness and efficiency over existing methods.

Findings

Estimators are less sensitive to outliers and heavy tails.

Simulation shows strong finite-sample performance.

Application demonstrates practical relevance in financial modeling.

Abstract

This paper proposes a robust and computationally efficient estimation framework for fitting parametric distributions based on trimmed L-moments. Trimmed L-moments extend classical L-moment theory by downweighting or excluding extreme order statistics, resulting in estimators that are less sensitive to outliers and heavy tails. We construct estimators for both location-scale and shape parameters using asymmetric trimming schemes tailored to different moments, and establish their asymptotic properties for inferential justification using the general structural theory of L-statistics, deriving simplified single-integration expressions to ensure numerical stability. State-of-the-art algorithms are developed to resolve the sign ambiguity in estimating the scale parameter for location-scale models and the tail index for the Frechet model. The proposed estimators offer improved efficiency over traditional robust alternatives for selected asymmetric trimming configurations, while retaining closed-form expressions for a wide range of common distributions, facilitating fast and stable computation. Simulation studies demonstrate strong finite-sample performance. An application to financial claim severity modeling highlights the practical relevance and flexibility of the approach.