A0629
Title: Low-rank covariance function estimation via functional unfolding
Authors: Jiayi Wang - Texas A and M University (United States)
Raymond Ka Wai Wong - Texas AM University (United States) [presenting]
Xiaoke Zhang - George Washington University (United States)
Abstract: Multidimensional function data arise from many fields nowadays. The covariance function plays an important role in the analysis of such increasingly common data. We will present a novel nonparametric covariance function estimation approach under the reproducing kernel Hilbert spaces (RKHS) framework that can handle both sparse and dense functional data. We extend multilinear rank structures for (finite-dimensional) tensors to functions, allowing for flexible modeling of covariance operators and marginal structures. The proposed framework can guarantee that the resulting estimator is automatically semi-positive definite and can incorporate various spectral regularizations. The trace-norm regularization, in particular, can promote low ranks for both covariance operator and marginal structures. Despite the lack of a closed-form, under mild assumptions, the proposed estimator can achieve unified theoretical results that hold for any relative magnitudes between the sample size and the number of observations per sample field. The rate of convergence reveals the phase-transition phenomenon from sparse to dense functional data.
