Abstract
This paper discusses two types of matrix by matrix derivatives; the B-type derivative, introduced by Balestra (1976) and the new defined A-type derivative, because of the arrangement in a “anti-Kronecker” type fashion. Both types of derivatives are linked by permutation matrices (also called commutation matrices by Magnus & Neudecker (1979)), a special type of 0/1-matrices. Section 2.1 gives a- short introduction to matrix derivatives, while the algebra of derivatives implied by these concepts can be found in Balestra (1976) and in Polasek (1980). A-and B-type derivatives allow different partitions of derivative matrices and therefore different ways of interpretations.
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References
Balestra, P. (1976), “La Dérivation Matricél le,” Collection de L′IME No. 12, Sirey, Paris
Chamberlain, G. and E. Learner (1976), “Matrix Weighted Averages and Posterior Bounds,” Journal of the Royal Statistical Society, Series B, 38, 73–84.
Dwyer, P.S. (1967), “Some Applications of Matrix Derivatives in Multivariate Analysis,” Journal of the American Statistical Association, 62, 607–625.
Leamer, E.E. (1972), “A Class of Informative Prior and Distributed Lag Analysis,” Econometrica, 42, 1059–1081.
Leamer, E.E. (1978), Specification Searches, New York: John- Wiley.
Magnus, J. R. and H. Nuedecker (1979), “A Class of Informative Prior and Distirbuted Lag Analysis,” Econometrica, 42, 1059–1081.
Mosteller, F. and J.W. Tukey (1977), Data Analysis and Regression, New York: Addison-Wes1ey.
Polasek, W. (1980) “Local Sensitivity Analysis in the General Linear Model”, University of Southern California, Department of Economics MRG #8006.
Tukey, J.W. (1977), Exploratory Data Analysis, New York: Addison- Wesley.
Zellner, A. (1962), “An Efficient Method of Estimating Seemingly Unrelated Regressions and Tests of Aggregation Bias,” Journal of the American Statistical Association, 57, 348–368.
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© 1982 D. Reidel Publishing Company
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Polasek, W. (1982). Local Sensitivity Analysis and Matrix Derivatives. In: Feichtinger, G., Kall, P. (eds) Operations Research in Progress. Theory and Decision Library, vol 32. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-7901-7_30
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DOI: https://doi.org/10.1007/978-94-009-7901-7_30
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