Proksch, Katharina

[["dc.bibliographiccitation.firstpage","283"],["dc.bibliographiccitation.lastpage","312"],["dc.bibliographiccitation.volume","134"],["dc.contributor.author","Munk, Axel"],["dc.contributor.author","Proksch, Katharina"],["dc.contributor.author","Li, Housen"],["dc.contributor.author","Werner, Frank"],["dc.contributor.editor","Salditt, Tim"],["dc.contributor.editor","Egner, Alexander"],["dc.contributor.editor","Luke, D. Russell"],["dc.date.accessioned","2021-03-05T08:58:56Z"],["dc.date.available","2021-03-05T08:58:56Z"],["dc.date.issued","2020"],["dc.identifier.doi","10.1007/978-3-030-34413-9_11"],["dc.identifier.eisbn","978-3-030-34413-9"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/80304"],["dc.notes.intern","DOI Import GROB-393"],["dc.publisher","Springer International Publishing"],["dc.publisher.place","Cham"],["dc.relation.eissn","1437-0859"],["dc.relation.isbn","978-3-030-34412-2"],["dc.relation.ispartof","Nanoscale Photonic Imaging"],["dc.relation.issn","0303-4216"],["dc.title","Photonic Imaging with Statistical Guarantees: From Multiscale Testing to Multiscale Estimation"],["dc.type","book_chapter"],["dc.type.internalPublication","unknown"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","1"],["dc.bibliographiccitation.journal","Journal of the American Statistical Association"],["dc.bibliographiccitation.lastpage","14"],["dc.contributor.author","Weitkamp, Christoph Alexander"],["dc.contributor.author","Proksch, Katharina"],["dc.contributor.author","Tameling, Carla"],["dc.contributor.author","Munk, Axel"],["dc.date.accessioned","2022-12-01T08:31:05Z"],["dc.date.available","2022-12-01T08:31:05Z"],["dc.date.issued","2022"],["dc.description.sponsorship"," Deutsche Forschungsgemeinschaft http://dx.doi.org/10.13039/501100001659"],["dc.description.sponsorship","DFG Research Training"],["dc.identifier.doi","10.1080/01621459.2022.2127360"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/118065"],["dc.language.iso","en"],["dc.notes.intern","DOI-Import GROB-621"],["dc.relation.eissn","1537-274X"],["dc.relation.issn","0162-1459"],["dc.title","Distribution of Distances based Object Matching: Asymptotic Inference"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","3569"],["dc.bibliographiccitation.issue","6B"],["dc.bibliographiccitation.journal","The Annals of Statistics"],["dc.bibliographiccitation.lastpage","3602"],["dc.bibliographiccitation.volume","46"],["dc.contributor.author","Proksch, Katharina"],["dc.contributor.author","Werner, Frank"],["dc.contributor.author","Munk, Axel"],["dc.date.accessioned","2017-09-07T11:50:35Z"],["dc.date.available","2017-09-07T11:50:35Z"],["dc.date.issued","2018"],["dc.description.abstract","In this paper we propose a multiscale scanning method to determine active components of a quantity f w.r.t. a dictionary U from observations Y in an inverse regression model Y=Tf+ξ with linear operator T and general random error ξ. To this end, we provide uniform confidence statements for the coefficients ⟨φ,f⟩, φ∈U, under the assumption that (T∗)−1(U) is of wavelet-type. Based on this we obtain a multiple test that allows to identify the active components of U, i.e. ⟨f,φ⟩≠0, φ∈U, at controlled, family-wise error rate. Our results rely on a Gaussian approximation of the underlying multiscale statistic with a novel scale penalty adapted to the ill-posedness of the problem. The scale penalty furthermore ensures weak convergence of the statistic's distribution towards a Gumbel limit under reasonable assumptions. The important special cases of tomography and deconvolution are discussed in detail. Further, the regression case, when T=id and the dictionary consists of moving windows of various sizes (scales), is included, generalizing previous results for this setting. We show that our method obeys an oracle optimality, i.e. it attains the same asymptotic power as a single-scale testing procedure at the correct scale. Simulations support our theory and we illustrate the potential of the method as an inferential tool for imaging. As a particular application we discuss super-resolution microscopy and analyze experimental STED data to locate single DNA origami."],["dc.identifier.arxiv","1611.04537"],["dc.identifier.doi","10.1214/17-AOS1669"],["dc.identifier.gro","3145901"],["dc.identifier.issn","0090-5364"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/3636"],["dc.language.iso","en"],["dc.notes.intern","lifescience"],["dc.notes.intern","Not valid abstract: In this paper we propose a multiscale scanning method to determine active components of a quantity $f$ w.r.t. a dictionary $\\\\.mathcal{U}$ from observations $Y$ in an inverse regression model $Y=Tf+\\\\.xi$ with operator $T$ and general random error $\\\\.xi$. To this end, we provide uniform confidence statements for the coefficients $\\\\.langle \\\\.varphi, f\\\\.rangle$, $\\\\.varphi \\\\.in \\\\.mathcal U$, under the assumption that $(T^*)^{-1} \\\\.left(\\\\.mathcal U\\\\.right)$ is of wavelet-type. Based on this we obtain a decision rule that allows to identify the active components of $\\\\.mathcal{U}$, i.e. $\\\\.left\\\\.langle f, \\\\.varphi\\\\.right\\\\.rangle \\\\.neq 0$, $\\\\.varphi \\\\.in \\\\.mathcal U$, at controlled, family-wise error rate. Our results rely on a Gaussian approximation of the underlying multiscale statistic with a novel scale penalty adapted to the ill-posedness of the problem. The important special case of deconvolution is discussed in detail. Further, the pure regression case, when $T = \\\\.ext{id}$ and the dictionary consists of moving windows of various sizes (scales), is included, generalizing previous results for this setting. Simulations support our theory and we illustrate the potential of the method as an inferential tool for imaging. As a particular application we discuss super-resolution microscopy and analyze experimental STED data to locate single DNA origami."],["dc.notes.status","public"],["dc.notes.submitter","chake"],["dc.subject","multiscale analysis scan statistic ill-posed problem deconvolution super-resolution"],["dc.title","Multiscale scanning in inverse problems"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]