2007/01/01 by Lukas Meier, Peter Bühlmann · 13 citations
Computer Science · Mathematics · #Adaptive estimator #Bayesian Methods and Mixture Models #Convergence (economics) #Estimator #Lasso (programming language) #Linear model #Machine Learning and Algorithms #Oracle #Rate of convergence #Smoothing #Statistical Methods and Inference #math.ST #msc:62H12 #msc:62J07 #msc:62J99 #stat.TH
paper · pdf · doi:10.1214/07-ejs103
published in Electronic Journal of Statistics 1(none) (Institute of Mathematical Statistics) · 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)
openalex publication_date 2007/01/01 · arxiv created 2007/12/11 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.