Geodesic
Estimation of the Kronecker and products of two mean vectors in multivariate analysis
Discussiones Mathematicae. Probability and Statistics, Tome 25 (2005) no. 2, pp. 207-215.

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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 multinormal distribution.
Keywords: multivariate normal distribution, Kronecker product, inner product, generalized jackknife, best unbiased estimator 
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Neudecker, Heinz; Trenkler, Götz. Estimation of the Kronecker and products of two mean vectors in multivariate analysis. Discussiones Mathematicae. Probability and Statistics, Tome 25 (2005) no. 2, pp. 207-215. http://geodesic.mathdoc.fr/item/DMPS_2005_25_2_a3/

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[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.