Statistical Methods for Mortality Modelling by Longitudinal and Functional Data Analysis

This thesis introduces several new statistical methods for mortality modelling under the background of longitudinal and functional data analysis. These are of high practical and methodological relevance, as the fundamental change in population structure in many countries, rising the needs of capturing the mortality trend trajectory and identifying critical factors correlated to mortality patterns. These require extensions of current statistical models with different structures and developments of entirely new statistical methods for mortality modelling. This thesis comprises four main topics, including three new extrapolative models and one new explanatory model for mortality modelling. We begin by reviewing the theoretical and methodological bases that contribute to the whole picture of this thesis. In the first topic, we extend and modify the structure of the CBD model with considerations of age groups dependence and random cohort effects as a time-series mixed-effects model for mortality modelling and prediction. In the second topic, we introduce a new non-parametric technique using Gaussian process regression with a natural cubic spline mean function and a spectral mixture covariance function for forecasts of mortality and fertility rates. In the third topic, we propose two new models for multiple populations mortality modelling and forecasting via multivariate functional principal component analysis. The first model extends the independent functional data model to a multi-population modelling setting. In the second one, we propose a novel multivariate functional principal component method for coherent modelling, which fulfils the idea that when several subpopulation groups have similar characteristics, such close connections are expected to evolve in a non-diversifying fashion. In the last topic, we extend and modify the traditional function-on-function regression model from a Bayesian perspective. We use it to investigate the influences of unemployment on mortality as an explanatory model. The thesis ends with a summary and a prospect for future research.