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 ℓ1-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.Comment: Published in at http://dx.doi.org/10.1214/07-EJS103 the Electronic
Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of
Mathematical Statistics (http://www.imstat.org