MINIMUM NORM ESTIMATION OF VARIANCE COMPONENTS FOR LIFE INSURANCE DATA

Life insurance companies want to predict the average claimed sums they have to pay in events of death for specific groups of customers in order to derive group specific premiums. This requires estimation of the variability of claims across groups. We derive a corresponding mixed linear model for claim data from many groups of customers that incorporates group-specific age distributions, the Compertz-Makeham mortality function and an unknown group-specific random hazard factor. It takes the form of a generalized replicated model with two variance components where the between blocks variance component depends on the common mean of all observations. Two methods of parameter estimation are derived along the lines of C. R. Rao's MINQUE and generalized least squares estimation. Simulations show both methods to work well for large sets of data.