Robust estimation and diagnostic of generalized linear model for insurance losses: a weighted likelihood approach

IF 0.9 4区 数学 Q3 STATISTICS & PROBABILITY
Metrika Pub Date : 2024-02-23 DOI:10.1007/s00184-024-00952-6
Tsz Chai Fung
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引用次数: 0

Abstract

This paper presents a score-based weighted likelihood estimator (SWLE) for robust estimations of the generalized linear model (GLM) for insurance loss data. The SWLE exhibits a limited sensitivity to the outliers, theoretically justifying its robustness against model contaminations. Also, with the specially designed weight function to effectively diminish the contributions of extreme losses to the GLM parameter estimations, most statistical quantities can still be derived analytically, minimizing the computational burden for parameter calibrations. Apart from robust estimations, the SWLE can also act as a quantitative diagnostic tool to detect outliers and systematic model misspecifications. Motivated by the coverage modifications which make insurance losses often random censored and truncated, the SWLE is extended to accommodate censored and truncated data. We exemplify the SWLE on three simulation studies and two real insurance datasets. Empirical results suggest that the SWLE produces more reliable parameter estimates than the MLE if outliers contaminate the dataset. The SWLE diagnostic tool also successfully detects any systematic model misspecifications with high power, accompanying some potential model improvements.

Abstract Image

保险损失广义线性模型的稳健估计和诊断:加权似然法
本文提出了一种基于分数的加权似然估计器(SWLE),用于对保险损失数据的广义线性模型(GLM)进行稳健估计。SWLE 对异常值的敏感度有限,从理论上证明了其对模型污染的稳健性。此外,由于专门设计的权重函数可有效降低极端损失对 GLM 参数估计的贡献,因此大多数统计量仍可通过分析得出,从而最大限度地减轻了参数校准的计算负担。除了稳健的估计之外,SWLE 还可以作为一种定量诊断工具,用于检测异常值和系统性模型错误规范。受保险范围修改的影响,保险损失往往是随机删减和截断的,因此我们对 SWLE 进行了扩展,以适应删减和截断数据。我们在三项模拟研究和两个真实保险数据集上对 SWLE 进行了示范。经验结果表明,如果数据集受到异常值的污染,SWLE 比 MLE 得出的参数估计结果更可靠。SWLE 诊断工具还能成功地检测出任何系统性的模型错误,并伴随着一些潜在的模型改进。
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来源期刊
Metrika
Metrika 数学-统计学与概率论
CiteScore
1.50
自引率
14.30%
发文量
39
审稿时长
6-12 weeks
期刊介绍: Metrika is an international journal for theoretical and applied statistics. Metrika publishes original research papers in the field of mathematical statistics and statistical methods. Great importance is attached to new developments in theoretical statistics, statistical modeling and to actual innovative applicability of the proposed statistical methods and results. Topics of interest include, without being limited to, multivariate analysis, high dimensional statistics and nonparametric statistics; categorical data analysis and latent variable models; reliability, lifetime data analysis and statistics in engineering sciences.
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