Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Application of covariance adjustment to seemingly unrelated multivariate regressions

  • Wang, Lichun (Department of Mathematics, Beijing Jiaotong University) ;
  • Pettit, Lawrence (School of Mathematical Sciences, Queen Mary University of London)
  • Received : 2018.02.27
  • Accepted : 2018.09.21
  • Published : 2018.11.30
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Abstract

Employing the covariance adjustment technique, we show that in the system of two seemingly unrelated multivariate regressions the estimator of regression coefficients can be expressed as a matrix power series, and conclude that the matrix series only has a unique simpler form. In the case that the covariance matrix of the system is unknown, we define a two-stage estimator for the regression coefficients which is shown to be unique and unbiased. Numerical simulations are also presented to illustrate its superiority over the ordinary least square estimator. Also, as an example we apply our results to the seemingly unrelated growth curve models.

Keywords

Acknowledgement

Supported by : NNSF

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