Robust and Computationally Efficient Trimmed L-Moments Estimation for Parametric Distributions
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910944839335936 |
|---|---|
| author | Poudyal, Chudamani Zhao, Qian Sitaula, Hari |
| author_facet | Poudyal, Chudamani Zhao, Qian Sitaula, Hari |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_09860 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Robust and Computationally Efficient Trimmed L-Moments Estimation for Parametric Distributions Poudyal, Chudamani Zhao, Qian Sitaula, Hari Methodology Statistics Theory Applications Computation 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. |
| title | Robust and Computationally Efficient Trimmed L-Moments Estimation for Parametric Distributions |
| topic | Methodology Statistics Theory Applications Computation |
| url | https://arxiv.org/abs/2505.09860 |