Consistencies and rates of convergence of jump-penalized least squares estimators

Simple item page
dc.creatorBoysen, Leif
dc.creatorKempe, Angela
dc.creatorLiebscher, Volkmar
dc.creatorMunk, Axel
dc.creatorWittich, Olaf
dc.date2009-02-27
dc.date.accessioned2026-07-07T12:47:35Z
dc.date.available2026-07-07T12:47:35Z
dc.descriptionWe study the asymptotics for jump-penalized least squares regression aiming at approximating a regression function by piecewise constant functions. Besides conventional consistency and convergence rates of the estimates in $L^2([0,1))$ our results cover other metrics like Skorokhod metric on the space of càdlàg functions and uniform metrics on $C([0,1])$. We will show that these estimators are in an adaptive sense rate optimal over certain classes of "approximation spaces." Special cases are the class of functions of bounded variation (piecewise) Hölder continuous functions of order $0<α\le1$ and the class of step functions with a finite but arbitrary number of jumps. In the latter setting, we will also deduce the rates known from change-point analysis for detecting the jumps. Finally, the issue of fully automatic selection of the smoothing parameter is addressed.
dc.descriptionPublished in at http://dx.doi.org/10.1214/07-AOS558 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/0902.4838
dc.identifierhttp://arxiv.org/abs/0902.4838
dc.identifierAnnals of Statistics 2009, Vol. 37, No. 1, 157-183
dc.identifierdoi:10.1214/07-AOS558
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/221773
dc.subjectStatistics Theory
dc.subject62G05, 62G20 (Primary) 41A10, 41A25 (Secondary)
dc.titleConsistencies and rates of convergence of jump-penalized least squares estimators
dc.typetext

Files

Collections

arXiv