Generalized estimating equations for variance and covariance parameters in regression credibility models

Abstract

We propose a regression credibility model that extends the one introduced by Hachemeister [Hachemeister, C.A., 1975. Credibility for regression models with application to trend. In: Kahn, P.M. (Ed.), Credibility: Theory and Applications. Academic Press, New York, pp. 129–163] by encapsulating a moving average error structure. Generalized estimating equations (GEE) are developed to estimate the unknown variance and covariance parameters. A comprehensive account is presented to demonstrate the implementation of the Bühlmann and Bühlmann–Straub frameworks under the model proposed and how GEE estimators are worked out within these two frameworks. A simulation study is conducted to compare the performance of the proposed GEE estimators with the alternative Bühlmann, Bühlmann–Straub, and Cossette and Luong’s [Cossette, H., Luong, A., 2003. Generalised least squares estimators for creditibilty regression models with moving average errors. Insurance Math. Econom. 32, 281–293] GLS estimators. The GEE estimators are found to perform well, especially when the error terms are correlated.