Consistent selection via the Lasso for high dimensional approximating regression models

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dc.creatorBunea, Florentina
dc.date2008-05-21
dc.date.accessioned2026-07-07T12:19:08Z
dc.date.available2026-07-07T12:19:08Z
dc.descriptionIn this article we investigate consistency of selection in regression models via the popular Lasso method. Here we depart from the traditional linear regression assumption and consider approximations of the regression function $f$ with elements of a given dictionary of $M$ functions. The target for consistency is the index set of those functions from this dictionary that realize the most parsimonious approximation to $f$ among all linear combinations belonging to an $L_2$ ball centered at $f$ and of radius $r_{n,M}^2$. In this framework we show that a consistent estimate of this index set can be derived via $\ell_1$ penalized least squares, with a data dependent penalty and with tuning sequence $r_{n,M}>\sqrt{\log(Mn)/n}$, where $n$ is the sample size. Our results hold for any $1\leq M\leq n^γ$, for any $γ>0$.
dc.descriptionPublished in at http://dx.doi.org/10.1214/074921708000000101 the IMS Collections (http://www.imstat.org/publications/imscollections.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/0805.3224
dc.identifierhttp://arxiv.org/abs/0805.3224
dc.identifierIMS Collections 2008, Vol. 3, 122-137
dc.identifierdoi:10.1214/074921708000000101
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/212646
dc.subjectStatistics Theory
dc.subjectMethodology
dc.subject62G08 (Primary) 62C20, 62G05, 62G20 (Secondary)
dc.titleConsistent selection via the Lasso for high dimensional approximating regression models
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