Title:   Recent developments in robust multivariate statistics

Abstract: 

In this short course we discuss two important topics in multivariate statistics: robust classification and cellwise outliers.

In the first part we study classification in the presence of outliers and mislabeled observations. Here, outlier refers to a case, that is, a row of the data matrix that behaves differently from the overall pattern. We study discriminant analysis based on robust estimates of location and scatter, such as the Minimum Covariance Determinant estimator (MCD). Next we introduce class maps and silhouette plots as graphical diagnostic plots for visualizing various aspects of classification results.

The second part addresses cellwise outliers. These are suspicious cells (entries) that can occur anywhere in the data matrix, and might not reveal themselves in the individual variables separately. We first describe the cellwise paradigm and address the detection of outlying cells. Then we look at a cellwise robust version of the MCD that can also deal with casewise outliers and missing values.

Keywords: cellwise outliers, classmaps, discriminant analysis, minimum covariance determinant, silhouette plot.

References:

Hubert, M., Raymaekers, J., Rousseeuw, P.J. (2024). Robust discriminant analysis. WIREs Computational Statistics, 16(5), e70003. https://arxiv.org/abs/2408.15701 

Raymaekers, J., Rousseeuw, P.J., Hubert, M. (2022). Class maps for visualizing classification results. Technometrics, 64, 151-165. https://www.tandfonline.com/doi/full/10.1080/00401706.2021.1927849 

Raymaekers, J., Rousseeuw, P.J. (2024). The Cellwise Minimum Covariance Determinant Estimator. Journal of the American Statistical Association, 119, 2610-2621. https://www.tandfonline.com/doi/full/10.1080/01621459.2023.2267777 

Rousseeuw, P.J., Van den Bossche, W. (2018). Detecting deviating data cells. Technometrics, 60, 135-145.  https://www.tandfonline.com/doi/full/10.1080/00401706.2017.1340909