{"title":"Data Depth: Robust Multivariate Analysis, Computational Geometry and Applications, Proceedings of a DIMACS Workshop, New Brunswick, New Jersey, USA, May 14-16, 2003","authors":"Regina Y. Liu, R. Serfling, D. Souvaine","doi":"10.1090/DIMACS/072","DOIUrl":"https://doi.org/10.1090/DIMACS/072","url":null,"abstract":"Depth functions in nonparametric multivariate inference by R. Serfling Rank tests for multivariate scale difference based on data depth by R. Y. Liu and K. Singh On scale curves for nonparametric description of dispersion by J. Wang and R. Serfling Data analysis and classification with the zonoid depth by K. Mosler and R. Hoberg On some parametric, nonparametric and semiparametric discrimination rules by A. Hartikainen and H. Oja Regression depth and support vector machine by A. Christmann Spherical data depth and a multivariate median by R. T. Elmore, T. P. Hettmansperger, and F. Xuan Depth-based classification for functional data by S. Lopez-Pintado and J. Romo Impartial trimmed means for functional data by J. A. Cuesta-Albertos and R. Fraiman Geometric measures of data depth by G. Aloupis Computation of half-space depth using simulated annealing by B. Chakraborty and P. Chaudhuri Primaldual algorithms for data depth by D. Bremner, K. Fukuda, and V. Rosta Simplicial depth: An improved definition, analysis, and efficiency for the finite sample case by M. A. Burr, E. Rafalin, and D. L. Souvaine Fast algorithms for frames and point depth by J. H. Dula Statistical data depth and the graphics hardware by S. Krishnan, N. H. Mustafa, and S. Venkatasubramanian.","PeriodicalId":161658,"journal":{"name":"Data Depth: Robust Multivariate Analysis, Computational Geometry and Applications","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128407477","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Depth-based classification for functional data","authors":"S. López-Pintado, J. Romo","doi":"10.1090/dimacs/072/08","DOIUrl":"https://doi.org/10.1090/dimacs/072/08","url":null,"abstract":"Classification is an important task when data are curves. Recently, the notion of statistical depth has been extended to deal with functional observations. In this paper, we propose robust procedures based on the concept of depth to classify curves. These techniques are applied to a real data example. An extensive simulation study with contaminated models illustrates the good robustness properties of these depth-based classification methods.","PeriodicalId":161658,"journal":{"name":"Data Depth: Robust Multivariate Analysis, Computational Geometry and Applications","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130539150","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Primal-dual algorithms for data depth","authors":"David Bremner, K. Fukuda, V. Rosta","doi":"10.1090/dimacs/072/12","DOIUrl":"https://doi.org/10.1090/dimacs/072/12","url":null,"abstract":"Note: PRO 060606 Reference ROSO-ARTICLE-2006-010 Record created on 2006-12-21, modified on 2016-08-08","PeriodicalId":161658,"journal":{"name":"Data Depth: Robust Multivariate Analysis, Computational Geometry and Applications","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126586744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Regression depth and support vector machine","authors":"A. Christmann","doi":"10.1090/dimacs/072/06","DOIUrl":"https://doi.org/10.1090/dimacs/072/06","url":null,"abstract":"The regression depth method (RDM) proposed by Rousseeuw and Hubert [RH99] plays an important role in the area of robust regression for a continuous response variable. Christmann and Rousseeuw [CR01] showed that RDM is also useful for the case of binary regression. Vapnik?s convex risk minimization principle [Vap98] has a dominating role in statistical machine learning theory. Important special cases are the support vector machine (SVM), [epsilon]-support vector regression and kernel logistic regression. In this paper connections between these methods from different disciplines are investigated for the case of pattern recognition. Some results concerning the robustness of the SVM and other kernel based methods are given.","PeriodicalId":161658,"journal":{"name":"Data Depth: Robust Multivariate Analysis, Computational Geometry and Applications","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133483839","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Rank tests for multivariate scale difference based on data depth","authors":"Regina Y. Liu, Kesar Singh","doi":"10.1090/dimacs/072/02","DOIUrl":"https://doi.org/10.1090/dimacs/072/02","url":null,"abstract":"","PeriodicalId":161658,"journal":{"name":"Data Depth: Robust Multivariate Analysis, Computational Geometry and Applications","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123846500","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Spherical data depth and a multivariate median","authors":"R. Elmore, T. Hettmansperger, F. Xuan","doi":"10.1090/dimacs/072/07","DOIUrl":"https://doi.org/10.1090/dimacs/072/07","url":null,"abstract":"","PeriodicalId":161658,"journal":{"name":"Data Depth: Robust Multivariate Analysis, Computational Geometry and Applications","volume":"179 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131572023","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Impartial trimmed means for functional data","authors":"J. A. Cuesta-Albertos, R. Fraiman","doi":"10.1090/dimacs/072/09","DOIUrl":"https://doi.org/10.1090/dimacs/072/09","url":null,"abstract":"","PeriodicalId":161658,"journal":{"name":"Data Depth: Robust Multivariate Analysis, Computational Geometry and Applications","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122364789","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Fast algorithms for frames and point depth","authors":"J. Dulá","doi":"10.1090/dimacs/072/14","DOIUrl":"https://doi.org/10.1090/dimacs/072/14","url":null,"abstract":"Foreword ix Preface xi Depth functions in nonparametric multivariate inference Robert Serfling 1 Rank tests for multivariate scale difference based on data depth Regina Y. Liu and Kesar Singh 17 On scale curves for nonparametric description of dispersion Jin Wang and Robert Serfling 37 Data analysis and classification with the zonoid depth Karl Mosler and Richard Hoberg 49 On some parametric, nonparametric and semiparametric discrimination rules Antti Hartikainen and Hannu Oja 61 Regression depth and support vector machine Andreas Christmann 71 Spherical data depth and a multivariate median Ryan T. Elmore, Thomas P. Hettmansperger, and Fengjuan Xuan 87 Depth-based classification for functional data Sara López-Pintado and Juan Romo 103 Impartial trimmed means for functional data Juan Antonio Cuesta-Albertos and Ricardo Fraiman 121 Geometric measures of data depth Greg Aloupis 147 Computation of half-space depth using simulated annealing Biman Chakraborty and Probal Chaudhuri 159 Primal-dual algorithms for data depth David Bremner, Komei Fukuda, and Vera Rosta 171 Simplicial depth: An improved definition, analysis, and efficiency for the finite sample case Michael A. Burr, Eynat Rafalin, and Diane L. Souvaine 195","PeriodicalId":161658,"journal":{"name":"Data Depth: Robust Multivariate Analysis, Computational Geometry and Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128434949","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Data analysis and classification with the zonoid depth","authors":"K. Mosler, R. Hoberg","doi":"10.1090/dimacs/072/04","DOIUrl":"https://doi.org/10.1090/dimacs/072/04","url":null,"abstract":"","PeriodicalId":161658,"journal":{"name":"Data Depth: Robust Multivariate Analysis, Computational Geometry and Applications","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123945677","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}