SUMMER SHAN

Title: An application of the James-Stein Estimation Method in Modeling of Mortality Rates
Date: Friday, September 22nd, 2023
Time: 9:30AM
Location: Hybrid (LIB 2020/ Zoom)
Supervised by: Dr. Cary Tsai

Abstract: 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 greater than or equal to 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 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, the Renshaw-Haberman model, and the maximum likelihood estimation method 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. Also, the modified James-Stein estimation method has stronger bias at younger and older ages due to shrinkage. As a result, the estimation error is larger at younger and older ages compared to the middle ages.

Keywords: James-Stein estimator; credibility theory; mortality model; Lee-Carter model; CBD model.