Hierarchical credibility pseudo-estimators

Abstract

Jewell's credibility model with two hierarchical levels and three variance parameters is treated. Under some additional assumptions, new pseudo-estimators are deduced, i.e. estimators which are defined by expressions that contain the estimands themselves and which must be solved numerically, for the parameters for variation between groups within sector and for variation between sectors. A Tweedie model is assumed for conditional claim rates, with exponent either 1 or 2, where 1 is for conditionally Poisson claim frequencies and 2 is for mean claim severities. Simulation results, where some of the additional assumptions are violated, indicate that our new pseudo-estimators are preferable over previous pseudo-estimators and non-pseudo-estimators for many cases that can be identified. The new between-sectors estimator seems to be universally better than the previous estimators. The goodness-of-fit of an estimator is measured by the square root of its mean square error relative to the true parameter.