Smoothing $\ell_1$-penalized estimators for high-dimensional time-course data

Details Smoothing $\ell_1$-penalized estimators for high-dimensional time-course data Smoothing $\ell_1$-penalized estimators for high-dimensional time-course data

2007-12-11

arxiv.org/abs/0712.1654v1

Electronic Journal of Statistics 2007, Vol. 1, 597-615

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/07-EJS103 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by t

Scientific paper

10.1214/07-EJS103

When a series of (related) linear models has to be estimated it is often appropriate to combine the different data-sets to construct more efficient estimators. We use $\ell_1$-penalized estimators like the Lasso or the Adaptive Lasso which can simultaneously do parameter estimation and model selection. We show that for a time-course of high-dimensional linear models the convergence rates of the Lasso and of the Adaptive Lasso can be improved by combining the different time-points in a suitable way. Moreover, the Adaptive Lasso still enjoys oracle properties and consistent variable selection. The finite sample properties of the proposed methods are illustrated on simulated data and on a real problem of motif finding in DNA sequences.

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