A Note on Choosing the Threshold for Large Covariance Estimations in Factor Models

2016/08/30 by Yuan Liao, Liao, Yuan
Economics, Econometrics and Finance · Mathematics · #FOS: Computer and information sciences #Methodology (stat.ME) #Spatial and Panel Data Analysis #Statistical Methods and Bayesian Inference #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.1608.08318

openalex publication_date 2016/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This note shows that for i.i.d. data, estimating large covariance matrices in factor models can be casted using a simple plug-in method to choose the threshold: μ_jl=(c₀)/(√(n))Φ^-1(1-\fracα2p²)√(1)/(n)∑_i=1ⁿ u_ji² u_li². This is motivated by the tuning parameter suggested by Belloni et al. (2012) in the lasso literature. It also leads to the minimax rate of convergence of the large covariance matrix estimator. Previously, the minimaxity is achievable only when n=o(plog p) by Fan et al. (2013), and now this condition is weakened to n=o(p²log p). Here n denotes the sample size and p denotes the dimension.

Citations

• Statistical Inferences Using Large Estimated Covariances for Panel Data and Factor Models

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