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Representations of best linear unbiased estimators in the Gauss-Markoff model with a singular dispersion matrix

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  • Rao, C. Radhakrishna

Abstract

In the general Gauss-Markoff model (Y, X[beta], [sigma]2V), when V is singular, there exist linear functions of Y which vanish with probability 1 imposing some restrictions on Y as well as on the unknown [beta]. In all earlier work on linear estimation, representations of best-linear unbiased estimators (BLUE's) are obtained under the assumption: "L'Y is unbiased for X[beta] => L'X = X." Such a condition is not, however, necessary. The present paper provides all possible representations of the BLUE's some of which violate the condition L'X = X. Representations of X for given classes of BLUE's are also obtained.

Suggested Citation

  • Rao, C. Radhakrishna, 1973. "Representations of best linear unbiased estimators in the Gauss-Markoff model with a singular dispersion matrix," Journal of Multivariate Analysis, Elsevier, vol. 3(3), pages 276-292, September.
    • Handle: RePEc:eee:jmvana:v:3:y:1973:i:3:p:276-292
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