Mixed estimation of old-age mortality

The estimation of the mortality of the “oldest old”; is subject to considerable random error, but important prior information exists that can be used to make the estimates more robust. Mixed estimation is a method of incorporating auxiliary information into the statistical estimation of linear models. We extend the method to cover general maximum likelihood estimation, and show that the mixed estimator can be represented approximately as a weighted average of the purely data based estimator and the auxiliary estimator. The methods can be applied to the analysis of the old-age mortality via logistic and Poisson regression. A major advantage of the mixed estimator is the simplicity with which it can incorporate partial prior information. Moreover, no special software is needed in the fitting. We show how the targeting methods of Coale and Kisker can be represented as mixed estimation in a natural way that is more flexible than the original proposal. We also derive empirical estimates of the target information based on pooled data from several countries with high quality data. We consider the mortality of Finland at ages 80 +, study the reliability of the evidence of mortality crossover, and derive estimates of life expectancy at age 100.