A0327
Title: Principal components analysis of correlated functional data
Authors: Julian Austin - Newcastle University (United Kingdom) [presenting]
Jian Qing Shi - Southern Univesity of Science and Technology (China)
Robin Henderson - Newcastle University (United Kingdom)
Abstract: A functional principal components analysis is considered where sparsely observed functional data exhibit correlation. We utilise penalised spline regression for estimation of both the mean and covariance surfaces. We account for between-curve correlation by correlating functional principal component scores using a Gaussian process to induce correlation. We consider the case of both stationary and non-stationary parametric covariance kernels for the Gaussian process. We propose a novel estimation procedure for the parametric covariance kernel using typical Gaussian process kernel estimation techniques. The performance of such a model is assessed on simulated sparsely observed functional data generated with various degrees of correlation from both stationary and non-stationary correlation structures. We show the proposed estimation procedure can reconstruct known hyperparameters of the various correlation structures well. We highlight the ability of such a model to identify dominant modes of variation and provide insight into the correlation structure between curves. We compare results to the principal components analysis assuming independent functional data and highlight the additional benefit for relaxing this assumption. Finally, we apply the method to spatio-temporal climate data.
