Discussiones Mathematicae Probability and Statistics 25(2) (2005) 207-215

ESTIMATION OF THE KRONECKER AND INNER PRODUCTS OF TWO MEAN VECTORS IN MULTIVARIATE ANALYSIS

Heinz Neudecker

Department of Econometrics, University of Amsterdam
Roetersstr. 11, NL-1018 WB Amsterdam, The Netherlands

Götz Trenkler

Department of Statistics, University of Dortmund
Vogelpothsweg 87, D-44221 Dortmund, Germany

Abstract

In this paper the Kronecker and inner products of mean vectorsof two different populations are considered. Using the generalized jackknife approach, estimators for these products are constructed which turn out to be unbiased, provided one can assume multinormaldistribution.

Keywords: multivariate normal distribution, Kronecker product, inner product, generalized jackknife, best unbiased estimator.

2000 Mathematics Subject Classification: Primary 62F10,Secondary 62F11.

References

[1] T.W. Anderson, An Introduction to Multivariate Statistical Analysis, John Wiley, New York 1984.
[2]A.G. Ghazal and H. Neudecker, On second-order and fourth-order moments of jointly distributed random matrices. A survey, Linear Algebra and Its Applications 321 (2000), 63-93.
[3] N.C. Giri, Multivariate Statistical Analysis, Marcel Dekker, New York 1996.
[4]H.L. Gray and W.R. Schucany, The Generalized Jackknife Statistics, Marcel Dekker, New York 1972.
[5]J.R. Magnus and H. Neudecker, Matrix Differential Calculus with Applications in Statistics and Econometrics, Wiley, New York 1988.

Received 14 May 2004