Minimizing cov(y - Fx)

Simo Puntanen (), George P. H. Styan () and Jarkko Isotalo ()
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Simo Puntanen: University of Tampere, School of Information Sciences
George P. H. Styan: McGill University, Department of Mathematics & Statistics
Jarkko Isotalo: University of Tampere, School of Information Sciences

Chapter Chapter 9 in Matrix Tricks for Linear Statistical Models, 2011, pp 191-214 from Springer

Abstract: Abstract In this chapter we consider the problem of finding the minimum—in the Löwner sense—for the covariance matrix of y - Fx where y and x are given random vectors and the matrix F is free to vary. This is a fundamental task in linear models and multivariate analysis and the solution, utilized in several places in this book, is very much worth remembering.

Keywords: Prediction Error; Random Vector; Conditional Expectation; Linear Predictor; Bivariate Normal Distribution (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-10473-2_10

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DOI: 10.1007/978-3-642-10473-2_10

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