Title: Covariance and graphical modelling for high-dimensional longitudinal and functional data
Authors: Xinghao Qiao - London School of Economics (United Kingdom)
Cheng Qian - London School of Economics and Political Science (United Kingdom) [presenting]
Abstract: The problem of estimating functional covariance and graphical models from a data set consisting of multivariate sparse longitudinal data is considered. The underlying trajectories are represented through the functional principal components expansions, where the covariance matrix of principal component scores characterizes the global covariance feature and principal component functions present the functional representation of covariance relationships. Our proposed estimation procedure first implements a nonparametric method to perform functional principal components for sparse longitudinal data, and then computes functional regularized covariance or precision matrices. We derive the relevant concentration inequalities for high dimensional sparsely sampled functional data and use them to investigate the uniform consistency results for our proposed estimators. The finite sample performance of our proposed methods are illustrated through an extensive set of simulation studies and two real data examples.