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Activity Number: 183
Type: Contributed
Date/Time: Monday, August 5, 2013 : 10:30 AM to 12:20 PM
Sponsor: WNAR
Abstract - #308177
Title: Efficient Estimation of Approximate Factor Models
Author(s): Yuan Liao*+ and Jushan Bai
Companies: University of Maryland and Columbia University
Keywords: unknown factors ; principal components ; conditional sparsity ; thresholding ; cross-sectional heteroskedasticity
Abstract:

In a high-dimensional approximate factor model, the regular principle components estimator does not efficiently estimate the parameters of the model. This paper proposes a method of generalized principle components (GPC), which relies on a high-dimensional weight matrix. Three important weights are compared: the identity matrix that gives the regular principle components estimator, the diagonal matrix with inverse cross-sectional variances that gives the heteroskedastic estimator, and the precision matrix of the error covariance that gives the efficient principle components estimator. We show that the precision error covariance is the optimal weight, which minimizes the asymptotic variance of the estimated common component. In order for the optimal GPC feasible, we assume a conditionally sparse structure of the model, and apply a thresholding estimator to consistently estimate the high-dimensional precision matrix. The feasible optimal GPC efficiently estimates the model parameters in the presence of both cross-sectional heteroskedasticity and dependence.


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