# Multivariate location and scatter matrix estimation under cellwise and casewise contamination

@article{Leung2017MultivariateLA, title={Multivariate location and scatter matrix estimation under cellwise and casewise contamination}, author={Andy Leung and Victor J. Yohai and Ruben H. Zamar}, journal={Comput. Stat. Data Anal.}, year={2017}, volume={111}, pages={59-76} }

We consider the problem of multivariate location and scatter matrix estimation when the data contain cellwise and casewise outliers. Agostinelli et al. (2015) propose a two-step approach to deal with this problem: first, apply a univariate filter to remove cellwise outliers and second, apply a generalized S-estimator to downweight casewise outliers. We improve this proposal in three main directions. First, we introduce a consistent bivariate filter to be used in combination with the univariate…

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## References

SHOWING 1-10 OF 20 REFERENCES

Robust estimation of multivariate location and scatter in the presence of cellwise and casewise contamination

- Mathematics, Computer Science
- 2014

The need for a new generation of robust estimators that can efficiently deal with cellwise outliers and at the same time show good performance under casewise outliers is highlighted.

Comments on: Robust estimation of multivariate location and scatter in the presence of cellwise and casewise contamination

- Computer Science
- 2015

This paper proposes an estimator that is specifically designed to tackle the combination of cellwise (ICM) and casewise (THCM) outliers and makes a point that the methods developed so far can handle one type of outliers or the other, but not yet both.

Comments on: Robust estimation of multivariate location and scatter in the presence of cellwise and casewise contamination

- Computer Science
- 2015

The authors deal with a very stimulating problem, that of robust location and scatter estimation in presence of cellwise and casewise outliers, and their proposed estimator provides an interesting solution to the problem.

Robust Estimation of Multivariate Location and Scatter in the Presence of Missing Data

- Mathematics
- 2012

Two main issues regarding data quality are data contamination (outliers) and data completion (missing data). These two problems have attracted much attention and research but surprisingly, they are…

Robust and efficient estimation of high dimensional scatter and location

- Mathematics
- 2015

We deal with the equivariant estimation of scatter and location for p-dimensional data, giving emphasis to scatter. It it important that the estimators possess both a high efficiency for normal data…

Multivariate Outlier Detection and Robust Covariance Matrix Estimation

- Computer ScienceTechnometrics
- 2001

A simple multivariate outlier-detection procedure and a robust estimator for the covariance matrix, based on the use of information obtained from projections onto the directions that maximize and minimize the kurtosis coefficient of the projected data are presented.

Propagation of outliers in multivariate data

- Mathematics
- 2009

We investigate the performance of robust estimates of multivariate location under nonstandard data contamination models such as componentwise outliers (i.e., contamination in each variable is…

Robustness properties of S-estimators of multivariate location and shape in high dimension

- Mathematics
- 1996

Author(s): Rocke, David | Abstract: For the problem of robust estimation of multivariate location and shape, defilllng S-estimators using scale transformations of a fixed p function regardless of the…

Robust Constrained Clustering in Presence of Entry-Wise Outliers

- Computer ScienceTechnometrics
- 2014

The method is robust to contamination, even when most or even all of the observations contain outliers, and global robustness of the resulting sclust procedure also when outliers arise entry-wise.

Scalable robust covariance and correlation estimates for data mining

- Mathematics, Computer ScienceKDD
- 2002

The estimators studied include two fast estimators based on coordinate-wise robust transformations embedded in an overall procedure recently proposed by [14] that have attractive robustness properties, and are given as an example that uses one of the estimators in the new Insightful Miner data mining product.