Modelling function‐valued stochastic processes, with applications to fertility dynamics

By Kehui Chen, Pedro Delicado, H. Muller. 2017

79 citations recorded by the source corpus.

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.

Subfields: Demography, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/9071278d0cb1d337b4052cc8440b827f3ae0e88a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Demography

1. Sang-Yun Oh
2. Alexander Petersen
3. Javier Zapata

In Statistics and Probability

1. Sang-Yun Oh
2. Alexander Petersen
3. Javier Zapata
4. H. Muller

Citations in the corpus

• Partial Separability and Functional Graphical Models for Multivariate Gaussian Processes (2019, methodology): “Motivated by recent work on dimension reduction and separability for so-called two-way functional data [1, 17, 4], we investigate similar separability notions for multivariate functional data.”