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Linear Regression in High Dimension and/or for Correlated Inputs

Published online by Cambridge University Press:  23 January 2015

J. Jacques  and
D. Fraix-Burnet
J. Jacques
Affiliation:
Université Lille 1 & CNRS & Inria, France
D. Fraix-Burnet
Affiliation:
Institut de Planétologie et d'Astrophysique de Grenoble (IPAG), France
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Abstract

Ordinary least square is the common way to estimate linear regression models. When inputs are correlated or when they are too numerous, regression methods using derived inputs directions or shrinkage methods can be efficient alternatives. Methods using derived inputs directions build new uncorrelated variables as linear combination of the initial inputs, whereas shrinkage methods introduce regularization and variable selection by penalizing the usual least square criterion. Both kinds of methods are presented and illustrated thanks to the R software on an astronomical dataset.

Type
Research Article
Information
European Astronomical Society Publications Series , Volume 66: Statistics for Astrophysics Methods and Applications of the Regression , 2014 , pp. 149 - 165
Copyright
© EAS, EDP Sciences, 2015

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