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Estimation of High-Dimensional Seemingly Unrelated Regression Models

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  • Lidan Tan
  • Khai X. Chiong
  • Hyungsik Roger Moon

Abstract

In this paper, we investigate seemingly unrelated regression (SUR) models that allow the number of equations (N) to be large, and to be comparable to the number of the observations in each equation (T). It is well known in the literature that the conventional SUR estimator, for example, the generalized least squares (GLS) estimator of Zellner (1962) does not perform well. As the main contribution of the paper, we propose a new feasible GLS estimator called the feasible graphical lasso (FGLasso) estimator. For a feasible implementation of the GLS estimator, we use the graphical lasso estimation of the precision matrix (the inverse of the covariance matrix of the equation system errors) assuming that the underlying unknown precision matrix is sparse. We derive asymptotic theories of the new estimator and investigate its finite sample properties via Monte-Carlo simulations.

Suggested Citation

  • Lidan Tan & Khai X. Chiong & Hyungsik Roger Moon, 2018. "Estimation of High-Dimensional Seemingly Unrelated Regression Models," Papers 1811.05567, arXiv.org.
    • Handle: RePEc:arx:papers:1811.05567
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    References listed on IDEAS

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    1. Jianqing Fan & Yuan Liao & Han Liu, 2016. "An overview of the estimation of large covariance and precision matrices," Econometrics Journal, Royal Economic Society, vol. 19(1), pages 1-32, February.
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    3. Li, Quan & Reuveny, Rafael, 2003. "Economic Globalization and Democracy: An Empirical Analysis," British Journal of Political Science, Cambridge University Press, vol. 33(1), pages 29-54, January.
    4. Cai, Tony & Liu, Weidong & Luo, Xi, 2011. "A Constrained â„“1 Minimization Approach to Sparse Precision Matrix Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 594-607.
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