For the purpose of explaining multivariate outlyingness, it is shown that squared Mahalanobis distance an observation can be decomposed into outlyingness contributions originating from single variables. The decomposition obtained using Shapley value, a well-known concept game theory became popular in context Explainable AI. In addition to outlier explanation, this also relates recent formulatio...

It is well known that if a multivariate outlier has one or more missing component values, then multiple imputation methods tend to impute non-extreme values and make the outlier become less extreme and less likely to be detected. In this paper, nonparametric depthbased multivariate outlier identifiers are used as criteria in a numerical study comparing several established methods of multiple im...

Multivariate Outlier Detection With High-Breakdown Estimators Andrea Cerioli Andrea Cerioli is Professor, Dipartimento di Economia, Sezione di Statistica e Informatica, Università di Parma, Via Kennedy 6, 43100 Parma, Italy . The author expresses his gratitude to three anonymous reviewers for insightful comments that led to many improvements in the article. The author also thanks Marco Riani an...

First of all, we would like to congratulate M. Hubert, P. Rousseeuw and P. Segaert for this very interesting and stimulating work. It is clear that functional data are becoming ubiquitous in many disciplines and the development of appropriate statistical techniques is clearly needed. Moreover, outliers are very likely to occur in this type of data, where many measurements are taken by applying ...

In this paper we propose a multivariate discount weighted regression technique to give a tractable solution to the problem of variance estimation and forecasting for the multivariate local level model. We give the correspondence between discount regression and matrix normal dynamic linear models and we show that the local level model can be treated with discount regression techniques. We illust...

This work focuses on detecting outliers within large and very large datasets using a computationally efficient procedure. The algorithm uses Tukey’s biweight function applied on the dataset to filter out the effects of extreme values for obtaining appropriate location and scale estimates. Robust Mahalanobis distances for all data points are calculated using these location and scale estimates. A...