Abstract
Multivariate linear model is a multivariate generalization for the dimension of response variable in traditional multiple linear regression model. This chapter provides some fundamental properties in terms of the multivariate linear model and the corresponding canonical form. The group invariance is also explained for shrinkage estimation in the multivariate linear model.
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References
T.W. Anderson, An Introduction to Multivariate Statistical Analysis, 3rd edn. (Wiley, New York, 2003)
M.L. Eaton, Multivariate Statistics: A Vector Space Approach (Wiley, New York, 1983)
M.L. Eaton, Group Invariance Application in Statistics. Regional Conference Series in Probability and Statistics, vol. 1 (Institute of Mathematical Statistics, Hayward, 1989)
E.L. Lehmann, G. Casella, Theory of Point Estimation, 2nd edn. (Springer, New York, 1998)
R.J. Muirhead, Aspects of Multivariate Statistical Theory (Wiley, New York, 1982)
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Tsukuma, H., Kubokawa, T. (2020). Multivariate Linear Model and Group Invariance. In: Shrinkage Estimation for Mean and Covariance Matrices. SpringerBriefs in Statistics(). Springer, Singapore. https://doi.org/10.1007/978-981-15-1596-5_4
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DOI: https://doi.org/10.1007/978-981-15-1596-5_4
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