Schuhmacher, Dominic

[["dc.bibliographiccitation.firstpage","1405"],["dc.bibliographiccitation.issue","1"],["dc.bibliographiccitation.journal","Electronic Journal of Statistics"],["dc.bibliographiccitation.lastpage","1437"],["dc.bibliographiccitation.volume","8"],["dc.contributor.author","Dümbgen, Lutz"],["dc.contributor.author","Rufibach, Kaspar"],["dc.contributor.author","Schuhmacher, Dominic"],["dc.date.accessioned","2017-09-07T11:50:30Z"],["dc.date.available","2017-09-07T11:50:30Z"],["dc.date.issued","2014"],["dc.description.abstract","We consider nonparametric maximum-likelihood estimation of a log-concave density in case of interval-censored, right-censored and binned data. We allow for the possibility of a subprobability density with an additional mass at +∞, which is estimated simultaneously. The existence of the estimator is proved under mild conditions and various theoretical aspects are given, such as certain shape and consistency properties. An EM algorithm is proposed for the approximate computation of the estimator and its performance is illustrated in two examples."],["dc.identifier.doi","10.1214/14-ejs930"],["dc.identifier.gro","3145885"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/3618"],["dc.notes.intern","mathe"],["dc.notes.status","public"],["dc.notes.submitter","chake"],["dc.publisher","Institute of Mathematical Statistics"],["dc.relation.issn","1935-7524"],["dc.subject","Active set algorithm binning cure parameter expectation-maximization algorithm interval-censoring qualitative constraints right-censoring"],["dc.title","Maximum-likelihood estimation of a log-concave density based on censored data"],["dc.type","journal_article"],["dc.type.internalPublication","unknown"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","376"],["dc.bibliographiccitation.issue","5-6"],["dc.bibliographiccitation.journal","Statistics & Probability Letters"],["dc.bibliographiccitation.lastpage","380"],["dc.bibliographiccitation.volume","80"],["dc.contributor.author","Schuhmacher, Dominic"],["dc.contributor.author","Dümbgen, Lutz"],["dc.date.accessioned","2017-09-07T11:50:32Z"],["dc.date.available","2017-09-07T11:50:32Z"],["dc.date.issued","2009"],["dc.description.abstract","This note proves Hellinger-consistency for the non-parametric maximum likelihood estimator of a log-concave probability density on RdRd."],["dc.identifier.doi","10.1016/j.spl.2009.11.013"],["dc.identifier.gro","3145892"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/3626"],["dc.notes.status","public"],["dc.notes.submitter","chake"],["dc.publisher","Elsevier BV"],["dc.relation.issn","0167-7152"],["dc.title","Consistency of multivariate log-concave density estimators"],["dc.type","journal_article"],["dc.type.internalPublication","unknown"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","78"],["dc.bibliographiccitation.lastpage","90"],["dc.bibliographiccitation.seriesnr","9"],["dc.contributor.author","Dümbgen, Lutz"],["dc.contributor.author","Samworth, Richard J."],["dc.contributor.author","Schuhmacher, Dominic"],["dc.date.accessioned","2017-09-07T11:50:34Z"],["dc.date.available","2017-09-07T11:50:34Z"],["dc.date.issued","2013"],["dc.description.abstract","This paper introduces and analyzes a stochastic search method for parameter estimation in linear regression models in the spirit of Beran and Millar (1987). The idea is to generate a random finite subset of a parameter space which will automatically contain points which are very close to an unknown true parameter. The motivation for this procedure comes from recent work of D¨umbgen, Samworth and Schuhmacher (2011) on regression models with log-concave error distributions."],["dc.identifier.arxiv","1106.3520"],["dc.identifier.doi","10.1214/12-imscoll907"],["dc.identifier.gro","3145888"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/3621"],["dc.notes.intern","mathe"],["dc.notes.status","public"],["dc.notes.submitter","chake"],["dc.publisher","Institute of Mathematical Statistics"],["dc.publisher.place","Beachwood, Ohio"],["dc.relation.crisseries","Institute of Mathematical Statistics Collections"],["dc.relation.isbn","978-0-940600-83-6"],["dc.relation.ispartof","From Probability to Statistics and Back: High-Dimensional Models and Processes"],["dc.relation.ispartofseries","Institute of Mathematical Statistics collections; 9"],["dc.title","Stochastic search for semiparametric linear regression models"],["dc.type","book_chapter"],["dc.type.internalPublication","unknown"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","277"],["dc.bibliographiccitation.issue","3"],["dc.bibliographiccitation.journal","Statistics & Risk Modeling"],["dc.bibliographiccitation.lastpage","295"],["dc.bibliographiccitation.volume","28"],["dc.contributor.author","Schuhmacher, Dominic"],["dc.contributor.author","Hüsler, André"],["dc.contributor.author","Dümbgen, Lutz"],["dc.date.accessioned","2017-09-07T11:50:32Z"],["dc.date.available","2017-09-07T11:50:32Z"],["dc.date.issued","2012"],["dc.description.abstract","In this paper we show that the family P_d of probability distributions on R^d with log-concave densities satisfies a strong continuity condition. In particular, it turns out that weak convergence within this family entails (i) convergence in total variation distance, (ii) convergence of arbitrary moments, and (iii) pointwise convergence of Laplace transforms. Hence the nonparametric model P_d has similar properties as parametric models such as, for instance, the family of all d-variate Gaussian distributions."],["dc.identifier.arxiv","0907.0250"],["dc.identifier.doi","10.1524/stnd.2011.1073"],["dc.identifier.gro","3145890"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/3624"],["dc.notes.intern","mathe"],["dc.notes.status","public"],["dc.notes.submitter","chake"],["dc.publisher","Walter de Gruyter GmbH"],["dc.relation.issn","2193-1402"],["dc.title","Multivariate log-concave distributions as a nearly parametric model"],["dc.type","journal_article"],["dc.type.internalPublication","unknown"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","702"],["dc.bibliographiccitation.issue","2"],["dc.bibliographiccitation.journal","Annals of statistics"],["dc.bibliographiccitation.lastpage","730"],["dc.bibliographiccitation.volume","39"],["dc.contributor.author","Dümbgen, Lutz"],["dc.contributor.author","Samworth, Richard"],["dc.contributor.author","Schuhmacher, Dominic"],["dc.date.accessioned","2017-09-07T11:50:35Z"],["dc.date.available","2017-09-07T11:50:35Z"],["dc.date.issued","2011"],["dc.description.abstract","We study the approximation of arbitrary distributions P on d-dimensional space by distributions with log-concave density. Approximation means minimizing a Kullback–Leibler-type functional. We show that such an approximation exists if and only if P has finite first moments and is not supported by some hyperplane. Furthermore we show that this approximation depends continuously on P with respect to Mallows distance D1(⋅, ⋅). This result implies consistency of the maximum likelihood estimator of a log-concave density under fairly general conditions. It also allows us to prove existence and consistency of estimators in regression models with a response Y=μ(X)+ε, where X and ε are independent, μ(⋅) belongs to a certain class of regression functions while ε is a random error with log-concave density and mean zero."],["dc.identifier.doi","10.1214/10-aos853"],["dc.identifier.gro","3145889"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/3622"],["dc.language.iso","en"],["dc.notes.intern","Not valid abstract: We study the approximation of arbitrary distributions P on d-dimensional space by distributions with log-concave density. Approximation means minimizing a Kullback–Leibler-type functional. We show that such an approximation exists if and only if P has finite first moments and is not supported by some hyperplane. Furthermore we show that this approximation depends continuously on P with respect to Mallows distance D1(·, ·). This result implies consistency of the maximum likelihood estimator of a log-concave density under fairly general conditions. It also allows us to prove existence and consistency of estimators in regression models with a response Y = μ(X)+\\\\., where X and \\\\. are independent, μ(·) belongs to a certain class of regression functions while \\\\. is a random error with logconcave density and mean zero."],["dc.notes.intern","mathe"],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.relation.issn","0090-5364"],["dc.subject","Convex support isotonic regression linear regression Mallows distance projection weak semicontinuity"],["dc.title","Approximation by log-concave distributions, with applications to regression"],["dc.type","journal_article"],["dc.type.internalPublication","no"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]