Modelling function‐valued stochastic processes, with applications to fertility dynamics. (17th February 2016)

• Record Type: Journal Article
• Authors: Chen, Kehui; Delicado, Pedro; Müller, Hans‐Georg
• Is Part Of: Journal of the Royal Statistical Society. Volume 79:Number 1(2017)
• Page Start: 177
• Page End: 196
• Publication Date: 2016-02-17
• Subjects: Asymptotics -- Demography -- Functional data analysis -- Marginal kernel -- Product principal component analysis -- Tensor product representation; Statistics -- Periodicals; Great Britain -- Statistics -- Periodicals; 519.2
• DOI: 10.1111/rssb.12160
• Languages: English
• ISSNs: 1369-7412

Abstract

Summary: We introduce a simple and interpretable model for functional data analysis for situations where the observations at each location are functional rather than scalar. This new approach is based on a tensor product representation of the function‐valued process and utilizes eigenfunctions of marginal kernels. The resulting marginal principal components and product principal components are shown to have nice properties. Given a sample of independent realizations of the underlying function‐valued stochastic process, we propose straightforward fitting methods to obtain the components of this model and to establish asymptotic consistency and rates of convergence for the estimates proposed. The methods are illustrated by modelling the dynamics of annual fertility profile functions for 17 countries. This analysis demonstrates that the approach proposed leads to insightful interpretations of the model components and interesting conclusions.