  A robust multilevel functional data method is proposed to forecast
age-specific mortality rate and life expectancy for two or more populations in
developed countries with high-quality vital registration systems. It uses a
robust multilevel functional principal component analysis of aggregate and
population-specific data to extract the common trend and population-specific
residual trend among populations. This method is applied to age- and
sex-specific mortality rate and life expectancy for the United Kingdom from
1922 to 2011, and its forecast accuracy is then further compared with standard
multilevel functional data method. For forecasting both age-specific mortality
and life expectancy, the robust multilevel functional data method produces more
accurate point and interval forecasts than the standard multilevel functional
data method in the presence of outliers.
