Luati, Alessandra and Proietti, Tommaso (2008): On the Spectral Properties of Matrices Associated with Trend Filters.
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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 eigen-decomposition of the associated smoothing matrix.
|Item Type:||MPRA Paper|
|Original Title:||On the Spectral Properties of Matrices Associated with Trend Filters|
|Keywords:||Signal extraction; Smoothing; Boundary conditions; Matrix algebras|
|Subjects:||C - Mathematical and Quantitative Methods > C2 - Single Equation Models; Single Variables > C22 - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models|
|Depositing User:||Tommaso Proietti|
|Date Deposited:||11. Nov 2008 03:33|
|Last Modified:||15. Feb 2013 01:00|
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