Robustness of Generalized Estimating Equations in Credibility Models

This dissertation, "Robustness of Generalized Estimating Equations in Credibility Models" by Danwei, Huang, 黃丹薇, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Abstract of thesis entitled ROBUSTNESS OF GENERALIZED ESTIMATING EQUATIONS IN CREDIBILITY MODELS Submitted by HUANG DAN WEI for the degree of Master of Philosophy at The University of Hong Kong in July 2007 Credibility theory is a branch of actuarial science. It provides tools to pre- dict future events or costs and helps the insurer adjust appropriately the premium charged to the policyholders. Since the insurance data can be interpreted in the context of statistical longitudinal data, there is a growing trend relating the cred- ibility theory and the generalized linear (mixed) model in parameter estimation. However, the generalized linear model (GLM) does not normally allow for serial correlation, which is a practical problem that needs to be addressed in the credi- bility context.As a supplement to the GLM in handling correlated data, a GEE (generalized estimating equations) approach has recently been proposed to estimate the struc- tural parameters in a regression credibility model which encapsulates a moving average error structure. Simulation results have shown that the GEE estimator performs well in comparison with the Buhlmann A estimator, the Buhlmann-Straub A estimatorandtheHachemeister'sestimator. ButintheGEEestimationprocedure, anormalityassumptionwasimposedandthecomparisonwasalsomadeinthenor- mal environment. When the normality assumption is violated, the performance of the GEE approach needs to be investigated. The study reported in this thesis aimed to check the robustness of the GEE es- timator in a non-normal environment. To sustain the estimation eciency, a mod- ication of the GEE estimation procedure is proposed to handle the high skewness and kurtosis of a non-normal distribution. Furthermore, diversied error structure assumptions are incorporated in the estimation procedure. The study considered the autoregressive and exchangeable error structures in addition to the moving average assumption, and estimation performances associated with these di(R)erent error structures were examined via simulation studies. In addition, the study also aimed to extend the application of the GEE method to another credibility model, the hierarchical credibility model. Derivation of the GEE estimator within the hi-erarchicalframeworkispresentedandnumericalexamplesareprovidedtofacilitate the comparison between the classical unbiased estimator and the GEE estimator. The study aimed to provide a thorough and comprehensive picture of the applica- tion of the GEE approach within the credibility context. DOI: 10.5353/th_b3884231 Subjects: Credibility theory (Insurance) Insurance - Mathematics