Title: Adaptive functional thresholding for sparse covariance matrix function estimation
Authors: Qin Fang - The London School of Economics and Political Science (United Kingdom) [presenting]
Xinghao Qiao - London School of Economics (United Kingdom)
Abstract: With the emergence of functional data in contemporary science and business, the problem of large covariance matrix function estimation arises in many applications. To consistently estimate covariance matrix function in high dimensions, we introduce a new class of functional thresholding operators, of which the thresholding and shrinkage conditions are imposed on function's Hilbert-Schmdit norm to encourage functional-sparsity, and propose an adaptive functional thresholding procedure of the sample covariance matrix function, taking into account the variability of functional entries. We further investigate the consistency and sparsistency of the proposed estimator. Monte Carlo simulations show the advantage of this estimator in terms of estimation accuracy and support recovery by comparing it with the universal functional thresholding estimator. As a motivating example, we study the functional connectivity using resting-state fMRI time-series data from two neuroscience datasets.