Nonparametric estimation of large covariance matrices with conditional sparsity

This paper studies estimation of covariance matrices with conditional sparse structure. We overcome the challenge of estimating dense matrices using a factor structure, the challenge of estimating large-dimensional matrices by postulating sparsity on covariance of random noises, and the challenge of estimating varying matrices by allowing factor loadings to smoothly change. A kernel-weighted estimation approach combined with generalised shrinkage is proposed. Under some technical conditions, we derive uniform consistency for the developed estimation method and obtain convergence rates. Numerical studies including simulation and an empirical application are presented to examine the finite-sample performance of the developed methodology.