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dc.contributor.authorDutta, Subhajit
dc.contributor.authorGenton, Marc G.
dc.date.accessioned2017-05-31T11:23:07Z
dc.date.available2017-05-31T11:23:07Z
dc.date.issued2017-04-05
dc.identifier.citationDutta S, Genton MG (2017) Depth-weighted robust multivariate regression with application to sparse data. Canadian Journal of Statistics 45: 164–184. Available: http://dx.doi.org/10.1002/cjs.11315.
dc.identifier.issn0319-5724
dc.identifier.doi10.1002/cjs.11315
dc.identifier.urihttp://hdl.handle.net/10754/623818
dc.description.abstractA robust method for multivariate regression is developed based on robust estimators of the joint location and scatter matrix of the explanatory and response variables using the notion of data depth. The multivariate regression estimator possesses desirable affine equivariance properties, achieves the best breakdown point of any affine equivariant estimator, and has an influence function which is bounded in both the response as well as the predictor variable. To increase the efficiency of this estimator, a re-weighted estimator based on robust Mahalanobis distances of the residual vectors is proposed. In practice, the method is more stable than existing methods that are constructed using subsamples of the data. The resulting multivariate regression technique is computationally feasible, and turns out to perform better than several popular robust multivariate regression methods when applied to various simulated data as well as a real benchmark data set. When the data dimension is quite high compared to the sample size it is still possible to use meaningful notions of data depth along with the corresponding depth values to construct a robust estimator in a sparse setting.
dc.description.sponsorshipWe are thankful to the editor, associate editor, and two anonymous referees for their useful comments which led to an improvement in the method and the article.
dc.publisherWiley
dc.relation.urlhttp://onlinelibrary.wiley.com/doi/10.1002/cjs.11315/full
dc.rightsThis is the peer reviewed version of the following article: Depth-weighted robust multivariate regression with application to sparse data, which has been published in final form at http://doi.org/10.1002/cjs.11315. This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.
dc.subjectData depth
dc.subjectLASSO
dc.subjectProjection depth
dc.subjectSpatial depth
dc.subjectWeighted averages
dc.titleDepth-weighted robust multivariate regression with application to sparse data
dc.typeArticle
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentStatistics Program
dc.identifier.journalCanadian Journal of Statistics
dc.eprint.versionPost-print
dc.contributor.institutionDepartment of Mathematics and Statistics; Indian Institute of Technology; Kanpur 208016 India
kaust.personGenton, Marc G.
refterms.dateFOA2018-04-05T00:00:00Z
dc.date.published-online2017-04-05
dc.date.published-print2017-06


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