Depth-weighted robust multivariate regression with application to sparse data
Type
ArticleAuthors
Dutta, SubhajitGenton, Marc G.

KAUST Department
Applied Mathematics and Computational Science ProgramComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Statistics Program
Date
2017-04-05Online Publication Date
2017-04-05Print Publication Date
2017-06Permanent link to this record
http://hdl.handle.net/10754/623818
Metadata
Show full item recordAbstract
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
WileyJournal
Canadian Journal of StatisticsAdditional Links
http://onlinelibrary.wiley.com/doi/10.1002/cjs.11315/fullae974a485f413a2113503eed53cd6c53
10.1002/cjs.11315