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Some Useful Matrix Lemmas in Statistical Estimation Theory*

Published online by Cambridge University Press:  20 November 2018

George C. Tiao  and
Irwin Guttman
George C. Tiao
Affiliation:
University of Wisconsin
Irwin Guttman
Affiliation:
University of Wisconsin
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In this note, we present two matrix lemmas (one without proof) which have interesting applications in statistical estimation theory.

LEMMA 1. Let A be a k X k positive definite matrix. Then for any k X 1 vector c, we have that

1.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 7 , Issue 2 , June 1964 , pp. 297 - 300
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Bhattacharya, A., On some analogues of the amount of information and their use in Statistical estimation, Sankhya, vol. 8 (1946), p. 1.Google Scholar
2. Box, G.E.P., Unpublished lecture notes, Department of Statistics, University of Wisconsin (1960).Google Scholar
3. Browne, E.T., Introduction to the Theory of Determinants and Matrices, University of North Carolina Press, (1958).Google Scholar
4. Kendall, M.G. and Stuart, A., The Advanced Theory of Statistics, Volume 2, Hafner (1961).Google Scholar
5. Lehmann, E.L., Notes on the Theory of Estimation, University of California Press, (1950).Google Scholar
6. Wilks, S.S., Mathematical Statistics, J. Wiley (1962).Google Scholar