On the natural restrictions in the singular Gauss–Markov model |
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| Authors: | Yongge Tian M Beisiegel E Dagenais C Haines |
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| Institution: | (1) School of Economics, Shanghai University of Finance and Economics, 777 Guoding Road, Shanghai, 200433, China;(2) Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada, T6G 2G1 |
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| Abstract: | A Gauss–Markov model is said to be singular if the covariance matrix of the observable random vector in the model is singular.
In such a case, there exist some natural restrictions associated with the observable random vector and the unknown parameter
vector in the model. In this paper, we derive through the matrix rank method a necessary and sufficient condition for a vector
of parametric functions to be estimable, and necessary and sufficient conditions for a linear estimator to be unbiased in
the singular Gauss–Markov model. In addition, we give some necessary and sufficient conditions for the ordinary least-square
estimator (OLSE) and the best linear unbiased estimator (BLUE) under the model to satisfy the natural restrictions.
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| Keywords: | Gauss– Markov model Estimability of parametric functions Unbiasedness of linear estimator Natural restriction Explicit restriction Matrix rank method OLSE BLUE |
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