2022/04/22 by Tsz Chai Fung, Fung, Tsz Chai
Agricultural and Biological Sciences · Mathematics · #Advanced Statistical Methods and Models #Agricultural risk and resilience #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Distribution Estimation and Applications
paper · pdf · doi:10.48550/arxiv.2204.10459
openalex publication_date 2022/04/22 · openalex created_date 2022/04/27 · openalex updated_date 2026/07/28
This paper presents a score-based weighted likelihood estimator (SWLE) for robust estimations of 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.