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ON THE SPECTRAL PROPERTIES OF MATRICES ASSOCIATED WITH TREND FILTERS

Published online by Cambridge University Press:  05 March 2010

Alessandra Luati  and
Tommaso Proietti
Alessandra Luati*
Affiliation:
University of Bologna
Tommaso Proietti
Affiliation:
University of Rome “Tor Vergata”
*
*Address correspondence to Alessandra Luati, Department of Statistics, University of Bologna, via Belle Arti 41, 40126 Bologna, Italy; e-mail: alessandra.luati@unibo.it.
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Abstract

This note is concerned with the spectral properties of matrices associated with linear smoothers. We derive analytical results on the eigenvalues and eigenvectors of smoothing matrices by interpreting the latter as perturbations of matrices belonging to algebras with known spectral properties, such as the circulant and the generalized tau. These results are used to characterize the properties of a smoother in terms of an approximate eigen-decomposition of the associated smoothing matrix.

Type
NOTES AND PROBLEMS
Information
Econometric Theory , Volume 26 , Issue 4 , August 2010 , pp. 1247 - 1261
Copyright
Copyright © Cambridge University Press 2010

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