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dc.contributor.authorBissantz, Nicolaien_US
dc.contributor.authorDümbgen, Lutzen_US
dc.contributor.authorMunk, Axelen_US
dc.contributor.authorStratmann, Bernden_US
dc.description.abstractThe computation of robust regression estimates often relies on minimization of a convex functional on a convex set. In this paper we discuss a general technique for a large class of convex functionals to compute the minimizers iteratively which is closely related to majorization-minimization algorithms. Our approach is based on a quadratic approximation of the functional to be minimized and includes the iteratively reweighted least squares algorithm as a special case. We prove convergence on convex function spaces for general coercive and convex functionals F and derive geometric convergence in certain unconstrained settings. The algorithm is applied to TV penalized quantile regression and is compared with a step size corrected Newton-Raphson algorithm. It is found that typically in the first steps the iteratively reweighted least squares algorithm performs significantly better, whereas the Newton type method outpaces the former only after many iterations. Finally, in the setting of bivariate regression with unimodality constraints we illustrate how this algorithm allows to utilize highly efficient algorithms for special quadratic programs in more complex settings.en_US
dc.publisher|aUniv., SFB 475|cDortmunden_US
dc.relation.ispartofseries|aTechnical Report // Sonderforschungsbereich 475, Komplexitätsreduktion in Multivariaten Datenstrukturen, Universität Dortmund|x2008,25en_US
dc.subject.keywordregression analysisen_US
dc.subject.keywordmonotone regressionen_US
dc.subject.keywordquantile regressionen_US
dc.subject.keywordshape constraintsen_US
dc.subject.keywordL1 regressionen_US
dc.subject.keywordnonparametric regressionen_US
dc.subject.keywordtotal variation semi-normen_US
dc.subject.keywordreweighted least squaresen_US
dc.subject.keywordFermat's problemen_US
dc.subject.keywordconvex approximationen_US
dc.subject.keywordquadratic approximationen_US
dc.subject.keywordpool adjacent violators algorithmen_US
dc.titleConvergence analysis of generalized iteratively reweighted least squares algorithms on convex function spacesen_US
dc.type|aWorking Paperen_US

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