Case Studies Using Credibility and Corrected Adaptively Truncated Likelihood Methods
By Harald Johann Dornheim, Vytaras Brazauskas
Two recent papers by Dornheim and Brazauskas (2011a, 2011b) introduced a new likelihood-based approach for robust-efficient fitting of mixed linear models and showed that it possesses favorable large and small-sample properties which yield more accurate premiums when extreme outcomes are present in the data. In particular, they studied regression-type credibility models that can be embedded within the framework of mixed linear models for which heavy-tailed insurance data are approximately log-location-scale distributed. The new methods were called corrected adaptively truncated likelihood methods (or CATL, for short). In this paper, we build upon that work and further explore how CATL methods can be used for pricing risks. We extend the area of application of standard credibility ratemaking to several well-studied examples from property and casualty insurance, health care, and real estate fields. The process of outlier identification, the ensuing model inference, and related issues are thoroughly investigated on the featured data sets. Throughout the case studies, performance of CATL methods is compared to that of other robust regression credibility procedures.
Keywords: Adaptive robust-efficient estimation, mixed linear model, outlier detection, prediction, regression credibility ratemaking