Abstract
Matrix algebra is an important step in mathematical treatment of shrinkage estimation for matrix parameters, and in particular the Moore-Penrose inverse and some matrix decompositions are required for defining matricial shrinkage estimators. This chapter first explains the notation used in this book and subsequently lists helpful results in matrix algebra.
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References
G.H. Golub, C.F. Van Loan, Matrix Computations, 3rd edn. (The Johns Hopkins University Press, Baltimore, 1996)
D.A. Harville, Matrix Algebra From a Statistician’s Perspective (Springer, New York, 1997)
J.R. Magnus, H. Neudecker, Matrix Differential Calculus with Applications in Statistics and Econometrics, 2nd edn. (Wiley, New York, 1999)
R.J. Muirhead, Aspects of Multivariate Statistical Theory (Wiley, New York, 1982)
C.R. Rao, Linear Statistical Inference and its Applications, 2nd edn. (Wiley, New York, 1973)
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Tsukuma, H., Kubokawa, T. (2020). Matrix Algebra. In: Shrinkage Estimation for Mean and Covariance Matrices. SpringerBriefs in Statistics(). Springer, Singapore. https://doi.org/10.1007/978-981-15-1596-5_2
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DOI: https://doi.org/10.1007/978-981-15-1596-5_2
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