COMPARISON OF MINQUE AND SIMPLE ESTIMATOR OF THE ERROR VARIANCE IN THE GAUSS MARKOFF MODEL
DOI:
https://doi.org/10.31642/JoKMC/2018/010106Keywords:
Gauss Markoff Model, MINQUE Mean, Simple EstimatorAbstract
The problem of estimation of variance components occurs in many areas of research. This paper is
devoted to study the comparison between Minimum Norm Quadratic Unbiased Estimator (MINQUE) and
Ordinary Least Square Estimator (OLSE) of s 2 in the Gauss Markoff Model {Y, Xb, s 2V}, under mean
square errors criterion, where the model matrix X need not have full rank and the dispersion matrix V can be singular.
A necessary and sufficient condition is obtained for that MINQUE is superior to simple estimator, in
particular, a simple sufficient condition is that the degree of freedom of errors is equal to or greater than 4.
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References
Dufour, J. (1986). Bias of S 2 in Linear Regressions with Dependent Errors. The
American Statistician, Vol. 40, No. 4, 284–285.
Graybill, F.A.(1983). Matrices with Applications in Statistics. University of California.
Belmont, California, Wadsworth.
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Copyright (c) 2023 Abdul-Hussein Saber AL-MOUEL
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