Luati, Alessandra and Proietti, Tommaso (2008): On the Spectral Properties of Matrices Associated with Trend Filters.

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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 generalised Tau. These results are used to characterise the properties of a smoother in terms of an approximate eigendecomposition of the associated smoothing matrix.
Item Type:  MPRA Paper 

Original Title:  On the Spectral Properties of Matrices Associated with Trend Filters 
Language:  English 
Keywords:  Signal extraction; Smoothing; Boundary conditions; Matrix algebras 
Subjects:  C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables > C22  TimeSeries Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes 
Item ID:  11502 
Depositing User:  Tommaso Proietti 
Date Deposited:  11. Nov 2008 03:33 
Last Modified:  15. Feb 2013 01:00 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/11502 