Robust and sparse estimation of high-dimensional precision matrices via bivariate outlier detection

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dc.contributor.author Lafit, Ginette
dc.contributor.author Nogales Martín, Francisco Javier
dc.contributor.other Universidad Carlos III de Madrid. Departamento de Estadística
dc.date.accessioned 2017-05-05T13:07:17Z
dc.date.available 2017-05-05T13:07:17Z
dc.date.issued 2017-05-01
dc.identifier.issn 2387-0303
dc.identifier.uri http://hdl.handle.net/10016/24534
dc.description.abstract Robust estimation of Gaussian Graphical models in the high-dimensional setting is becoming increasingly important since large and real data may contain outlying observations. These outliers can lead to drastically wrong inference on the intrinsic graph structure. Several procedures apply univariate transformations to make the data Gaussian distributed. However, these transformations do not work well under the presence of structural bivariate outliers. We propose a robust precision matrix estimator under the cellwise contamination mechanism that is robust against structural bivariate outliers. This estimator exploits robust pairwise weighted correlation coefficient estimates, where the weights are computed by the Mahalanobis distance with respect to an affine equivariant robust correlation coefficient estimator. We show that the convergence rate of the proposed estimator is the same as the correlation coefficient used to compute the Mahalanobis distance. We conduct numerical simulation under different contamination settings to compare the graph recovery performance of different robust estimators. Finally, the proposed method is then applied to the classification of tumors using gene expression data. We show that our procedure can effectively recover the true graph under cellwise data contamination.
dc.description.sponsorship Acknowledgements: the authors acknowledge financial support from the Spanish Ministry of Education and Science, research project MTM2013-44902-P.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.relation.ispartofseries UC3M Working Papers Statistics and Econometrics
dc.relation.ispartofseries 17-06
dc.rights Atribución-NoComercial-SinDerivadas 3.0 España
dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject.other Gaussian graphical models
dc.subject.other Cellwise contamination
dc.subject.other Robust correlation estimation
dc.subject.other Winsorization
dc.title Robust and sparse estimation of high-dimensional precision matrices via bivariate outlier detection
dc.type workingPaper
dc.relation.projectID Gobierno de España. MTM2013-44902-P
dc.identifier.uxxi DT/0000001545
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