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    Depth-weighted robust multivariate regression with application to sparse data

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    Type
    Article
    Authors
    Dutta, Subhajit
    Genton, Marc G. cc
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Statistics Program
    Date
    2017-04-05
    Online Publication Date
    2017-04-05
    Print Publication Date
    2017-06
    Permanent link to this record
    http://hdl.handle.net/10754/623818
    
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    Abstract
    A 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.
    Citation
    Dutta 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.
    Sponsors
    We 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.
    Publisher
    Wiley
    Journal
    Canadian Journal of Statistics
    DOI
    10.1002/cjs.11315
    Additional Links
    http://onlinelibrary.wiley.com/doi/10.1002/cjs.11315/full
    ae974a485f413a2113503eed53cd6c53
    10.1002/cjs.11315
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Statistics Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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