Bai, Jushan and Liao, Yuan (2012): Efficient Estimation of Approximate Factor Models via Regularized Maximum Likelihood.
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Abstract
We study the estimation of a high dimensional approximate factor model in the presence of both cross sectional dependence and heteroskedasticity. The classical method of principal components analysis (PCA) does not efficiently estimate the factor loadings or common factors because it essentially treats the idiosyncratic error to be homoskedastic and cross sectionally uncorrelated. For the efficient estimation, it is essential to estimate a large error covariance matrix. We assume the model to be conditionally sparse, and propose two approaches to estimating the common factors and factor loadings; both are based on maximizing a Gaussian quasilikelihood and involve regularizing a large covariance sparse matrix. In the first approach the factor loadings and the error covariance are estimated separately while in the second approach they are estimated jointly. Extensive asymptotic analysis has been carried out. In particular, we develop the inferential theory for the twostep estimation. Because the proposed approaches take into account the large error covariance matrix, they produce more efficient estimators than the classical PCA methods or methods based on a strict factor model.
Item Type:  MPRA Paper 

Original Title:  Efficient Estimation of Approximate Factor Models via Regularized Maximum Likelihood 
Language:  English 
Keywords:  High dimensionality; unknown factors; principal components; sparse matrix; conditional sparse; thresholding; crosssectional correlation; penalized maximum likelihood; adaptive lasso; heteroskedasticity 
Subjects:  C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models; Multiple Variables > C31  CrossSectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models; Multiple Variables > C33  Models with Panel Data; Longitudinal Data; Spatial Time Series C  Mathematical and Quantitative Methods > C0  General > C01  Econometrics 
Item ID:  41641 
Depositing User:  Yuan Liao 
Date Deposited:  01. Oct 2012 13:40 
Last Modified:  13. Feb 2013 16:35 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/41641 
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Efficient Estimation of Approximate Factor Models. (deposited 26. Sep 2012 14:27)
 Efficient Estimation of Approximate Factor Models via Regularized Maximum Likelihood. (deposited 01. Oct 2012 13:40) [Currently Displayed]