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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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
Keywords
- Gauss–Markov model
- Estimability of parametric functions
- Unbiasedness of linear estimator
- Natural restriction
- Explicit restriction
- Matrix rank method
- OLSE
- BLUE