Robust estimation and model diagnostic of insurance loss data: a weighted likelihood approach

TL;DR

This paper introduces a robust weighted likelihood estimator for insurance loss data that effectively reduces outlier influence, improves parameter estimation reliability, and detects model misspecifications, especially in censored or truncated datasets.

Contribution

The paper develops a score-based weighted likelihood estimator (SWLE) that enhances robustness against outliers and model contamination in insurance loss data, with analytical derivations and diagnostic capabilities.

Findings

SWLE outperforms MLE in contaminated datasets.

SWLE effectively detects outliers and model misspecifications.

The method extends to censored and truncated insurance data.

Abstract

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.