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On efficient estimators of two seemingly unrelated regressions
Authors:Lichun Wang  Heng LianRadhey S Singh
Institution:
  • a Department of Mathematics, Beijing Jiaotong University, Beijing 100044, PR China
  • b Division of Mathematical Sciences, SPMS, Nanyang Technological University, Singapore 637371, Singapore
  • c Department of Mathematics & Statistics, University of Guelph, Guelph, Ontario, Canada
  • Abstract:In this paper, following the results presented in Liu’s work Liu, A.Y., 2002. Efficient estimation of two seemingly unrelated regression equations. Journal of Multivariate Analysis 82, 445-456], we first represent the Gauss-Markov estimator of the regression parameter as a matrix series, and hence we conclude that the observation vectors should appear in any efficient estimator in pairs. Second, we prove that the simpler form of the two-stage Aitken estimator is unique. Finally we generalize our results to the system of two seemingly unrelated regressions with unequal numbers of observations and briefly summarize our conclusions.
    Keywords:62J05  62F10
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