Factor-guided estimation of large covariance matrix function with conditional functional sparsity
4 November 2023
Proposes DIGIT and FPOET estimators for covariance matrices of high-dimensional functional data under two factor model frameworks
Assumes sparsity in idiosyncratic error covariance after accounting for latent factors
Performs eigenanalysis or functional PCA to estimate common components, then thresholds residuals
Establishes asymptotic convergence rates under functional matrix norms
Shows superior performance over competitors in simulations and real data applications
Estimating covariance matrices for high-dimensional functional data using factor models
This paper develops methods to estimate covariance matrix functions for high-dimensional functional data or functional time series. It considers two types of functional factor models, one with functional factors and scalar loadings, the other with scalar factors and functional loadings. By assuming sparsity in the idiosyncratic error covariance after accounting for common factors, the paper proposes DIGIT and FPOET estimators. These perform eigenanalysis or functional PCA to estimate the covariance of common components, then apply adaptive thresholding to the residuals. Asymptotic theory is provided, showing these achieve consistent estimation under functional matrix norms. Simulations and applications to mortality rates and stock returns demonstrate the methods outperform competitors.
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