Groupe d’études et de recherche en analyse des décisions

Data Depth: Theory, Computations and Applications

Shojaeddin Chenouri

In multivariate inference, data often cannot be modeled by normal or, more general, elliptically symmetric distributions. Then the classical multivariate analysis which relies heavily on the assumption of normality or near normality (ellipticity), fails. These assumptions also are often difficult to justify in practice.

The goal of this talk is to give an introduction to the recent advancements in multivariate nonparametric inference and data analysis based on the concept of data depth. A data depth is a measure of how deep or outlying a given point is with respect to a data cloud or a distribution. Depth functions introduce center-outward orderings and rankings of multidimensional data.

In this talk, we shall review briefly different notions of data depth, the associated multidimensional medians, and their statistical properties and computational complexities. Along with examples we shall discuss some graphical techniques for the multivariate goodness of fit, multivariate dispersion, etc. We also construct families of nonparametric multivariate multi-sample location and dispersion tests. To conclude, some other applications of data depth in multivariate data analysis and also research topics related to the notion of data depth will be discussed.