Abstract
In this chapter, we shall consider the LSD of a product of two random matrices, one of them a sample covariance matrix and the other an arbitrary Hermitian matrix. This topic is related to two areas: The first is the study of the LSD of a multivariate F-matrix that is a product of a sample covariance matrix and the inverse of another sample covariance matrix, independent of each other. Multivariate F plays an important role in multivariate data analysis, such as two-sample tests, MANOVA (multivariate analysis of variance), and multivariate linear regression. The second is the investigation of the LSD of a sample covariance matrix when the population covariance matrix is arbitrary. The sample covariance matrix under a general setup is, as mentioned in Chapter 3, fundamental in multivariate analysis.
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© 2010 Springer Science+Business Media, LLC
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Bai, Z., Silverstein, J.W. (2010). Product of Two Random Matrices. In: Spectral Analysis of Large Dimensional Random Matrices. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-0661-8_4
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DOI: https://doi.org/10.1007/978-1-4419-0661-8_4
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Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-0660-1
Online ISBN: 978-1-4419-0661-8
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