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On the extensions of Gauss-Markov theorem to subsets of the parameter space under complex multivariate linear models

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Summary

In this paper we continue the study of the extension of the Gauss-Markov theorem to certain general kinds of multiresponse models. In particular we obtain necessary and sufficient conditions, for the general incomplete multiresponse (GIM) model and the multiple design multi-response (MDM) model, such that unique best linear unbiased estimates (BLUE's) exist for all elements in a subset of the set of all estimable linear functions of the location parameters. Also the theory is illustrated by a couple of nontrivial examples.

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References

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Authors and Affiliations

  1. Colorado State University, Colorado, USA

    J. N. Srivastava & Lyman L. McDonald

  2. University of Wyoming, Wyoming, USA

    J. N. Srivastava & Lyman L. McDonald

Authors
  1. J. N. Srivastava
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  2. Lyman L. McDonald
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Additional information

This research was wholly supported by the U.S. Air Force under grant No. F33615-67-C-1436, monitored by the Aerospace Research Laboratories.

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Srivastava, J.N., McDonald, L.L. On the extensions of Gauss-Markov theorem to subsets of the parameter space under complex multivariate linear models. Ann Inst Stat Math 25, 383–393 (1973). https://doi.org/10.1007/BF02479384

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  • DOI: https://doi.org/10.1007/BF02479384

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