Estimation of structural parameters for panel data in credibility context
Abstract of thesis entitled
ESTIMATION OF STRUCTURAL
PARAMETERS FOR PANEL DATA IN
Submitted by LO CHI HO
for the degree of Master of Philosophy
at The University of Hong Kong in August 2005
Credibility theory is a popular topic in insurance for the sake of determination of the premium level of a risk entity. While the majority of theoretical developments in credibility context stems from an independent error assumption, from a practical point of view the consecutive error terms with regard to the observations of a risk entity are usually correlated. The aim of this thesis study is to examine a convenient approach for estimating the structural parameters of a regression credibility model with the presence of an assumed correlation structure for the error terms.
A regression credibility model, which encapsulates a correlated error structure, is proposed. It is used to implement classical credibility frameworks, namely, Bu?lmann, Bu?lmann-Straub and Hachemeister, extended to a moving average
error structure. Estimators using generalized estimating equations (GEE) have been developed for the unknown structural parameters in the model. It shows that the classical Bu?lmann estimators can be replicated using the proposed GEE approach. In contrast to a previous work of Cossette and Luong, which utilizes a generalized least square (GLS) approach for parameter estimation, the proposed GEE approach has an advantage that it can address to variations in exposures and the observed values of the covariates across entities, and, henceforth, exercise fully the Bu?lmann-Straub and Hachemeister frameworks. A simulation study was conducted to compare the performance of the proposed GEE estimators with alternatives including Bu?lmann, Bu?lmann-Straub, Cossette and Luong? GLS and Hachemeister estimators. The results suggest that proposed GEE estimators have improved remarkably the accuracy of the estimators for the structural parameters and the credibility estimators so constructed, especially when the error terms are correlated.
School:The University of Hong Kong
School Location:China - Hong Kong SAR
Source Type:Master's Thesis
Keywords:credibility theory insurance claims mathematical models
Date of Publication:01/01/2005