An Application of the James-Stein Estimation Method in Modeling of Mortality Rates

It is known that the James-Stein estimation method outperforms the Maximum Likelihood Estimation method when we estimate a p−dimension independently distributed random variable with p ≥ 3. In this project, an explicit formula based on a modified James-Stein estimation is first derived to forecast a p−dimension random variable. Then the modified James-Stein estimator is applied to forecasting of mortality rates for 10, 20 and 30 years for six populations (both genders of the U.S., the U.K., and Japan). Moreover, some underlying mortality models (the Lee-Carter model, the Cairns-Blake-Dowd model, the M6 and M7 models, and the Renshaw-Haberman model) are also used in the forecasting of mortality rates to compare their forecast performances with the modified James-Stein estimation method. The results show that the modified James-Stein estimation method has the lowest overall average estimation error compared to all other mortality models. Finally, the shrinkage effect of the modified James-Stein estimate is studied with numerical illustrations for six populations and three forecasting years.