Hostname: page-component-745bb68f8f-b95js Total loading time: 0 Render date: 2025-01-12T23:04:29.708Z Has data issue: false hasContentIssue false
  • English
  • Français

On Unbiased Estimation of a Vector Parameter

Published online by Cambridge University Press:  20 November 2018

K. L. Mehra  and
P. V. Ramachandramurty
K. L. Mehra
Affiliation:
University of Alberta, Edmonton, Alberta
P. V. Ramachandramurty
Affiliation:
University of Alberta, Edmonton, Alberta
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

It is shown in this paper that Rao's criterion of comparing two unbiased estimators on the basis of definiteness of the difference between their dispersion matrices is equivalent to Cramer's criterion based on their concentration ellipsoids. When the estimators have normal distributions it is shown that both the criteria have a desirable property in terms of the probabilities of the estimators lying in ellipsoids with the parameter point as the center.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 15 , Issue 4 , December 1972 , pp. 547 - 550
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Harold, Cramer, Mathematical methods of statistics, Princeton Univ. Press, Princeton, N.J., 1946.Google Scholar
2. Rao, C. R., Minimum variance and the estimation of several parameters, Proc. Cambridge Philos. Soc. 43 (1947), 280-283.Google Scholar
3. Rao, C. R., Linear statistical inference and its applications, Wiley, New York, 1965.Google Scholar
4. Henry, Scheffe, Analysis of variance, Wiley, New York, 1959.Google Scholar
5. Wilks, S. S., Certain generalisations in the analysis of variance, Biometrika 24 (1932), 471-494.Google Scholar