Array methods in statistics with applications to the modelling and forecasting of mortality

Abstract

In this thesis we investigate the application of array methods for the smoothing of multi-dimensional arrays with particular reference to mortality data. A broad outline follows. We begin with an introduction to smoothing in one dimension, followed by a discussion of multi-dimensional smoothing methods. We then move on to review and develop the array methods of Currie et al. (2006), and show how these methods can be applied in additive models even when the data do not have a standard array structure. Finally we discuss the Lee-Carter model and show how we fulfilled the requirements of the CASE studentship. Our main contributions are: firstly we extend the array methods of Currie et al. (2006) to cope with more general covariance structures; secondly we describe an additive model of mortality which decomposes the mortality surface into a smooth twodimensional surface and a series of smooth age dependent shocks within years; thirdly we describe an additive model of mortality for data with a Lexis triangle structure.