On efficient estimators of two seemingly unrelated regressions |
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Authors: | Lichun Wang Heng LianRadhey S Singh |
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Institution: | a Department of Mathematics, Beijing Jiaotong University, Beijing 100044, PR Chinab Division of Mathematical Sciences, SPMS, Nanyang Technological University, Singapore 637371, Singaporec Department of Mathematics & Statistics, University of Guelph, Guelph, Ontario, Canada |
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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. |
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Keywords: | 62J05 62F10 |
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