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On the natural restrictions in the singular Gauss–Markov model

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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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Authors and Affiliations

  1. School of Economics, Shanghai University of Finance and Economics, 777 Guoding Road, Shanghai, 200433, China

    Yongge Tian

  2. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada, T6G 2G1

    M. Beisiegel, E. Dagenais & C. Haines

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  1. Yongge Tian
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  2. M. Beisiegel
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  3. E. Dagenais
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  4. C. Haines
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Correspondence to Yongge Tian.

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Tian, Y., Beisiegel, M., Dagenais, E. et al. On the natural restrictions in the singular Gauss–Markov model. Statistical Papers 49, 553–564 (2008). https://doi.org/10.1007/s00362-006-0032-5

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  • DOI: https://doi.org/10.1007/s00362-006-0032-5

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