TY - JOUR
T1 - Depth-weighted robust multivariate regression with application to sparse data
AU - Dutta, Subhajit
AU - Genton, Marc G.
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: 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.
PY - 2017/4/5
Y1 - 2017/4/5
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/623818
UR - http://onlinelibrary.wiley.com/doi/10.1002/cjs.11315/full
UR - http://www.scopus.com/inward/record.url?scp=85017220390&partnerID=8YFLogxK
U2 - 10.1002/cjs.11315
DO - 10.1002/cjs.11315
M3 - Article
VL - 45
SP - 164
EP - 184
JO - Canadian Journal of Statistics
JF - Canadian Journal of Statistics
SN - 0319-5724
IS - 2
ER -