A0596
Title: Exponential-family principal component analysis of two-dimensional functional data with serial correlation
Authors: Kejun He - Renmin University of China (China) [presenting]
Bohai Zhang - Nankai University (China)
Lan Zhou - Texas A and M University (United States)
Abstract: Motivated by a study on Arctic sea-ice-extent (SIE) data of binary observations, a novel model is proposed to analyze serially correlated non-Gaussian data observed on a two-dimensional domain that may have an irregular shape. The observed data is assumed to follow a distribution from the exponential family, where the corresponding natural parameter is a dynamic, smooth function of two-dimensional locations. A functional principal component model using bivariate splines defined on triangulations is applied on the natural-parameter surface to characterize the spatial variation of data. Autoregressive (AR) processes model the serial correlation of data observed at consecutive time points on the principal component scores. To estimate the unknown parameters, an EM algorithm is developed with two approaches, using Laplace approximation and variational inference, respectively, on the E-step. Through simulation studies, it is found that the latter is much faster with higher estimation accuracy, especially when the sample size is large. Finally, the proposed model with variational inference EM algorithm is applied to analyze the massive monthly Arctic SIE data.
