Davy Paindaveine (ULB): An excursion through statistical depth

Thursday 26 Oct 2017, 16:30 → 18:00 Europe/Brussels

CYCL 01 (Marc de Hemptinne)

Statistical depth aims at measuring centrality of any given location in the d-dimensional Euclidean space with respect to probability distributions over this space. For empirical distributions, depth provides (i) a deepest point, that usually can be seen as a multivariate median, and (ii) a center-outward ordering of the observations. Depth may therefore be considered as a concept of multivariate ranks. In this lecture, we will introduce the main concepts of depth, including Tukey's halfspace depth and Liu's simplicial depth. We will present some well-known properties and discuss Serfling's axiomatic approach. We will then briefly describe some inferential applications of depth. If time permits, the strong relation between depth and multivariate quantiles will be examined, and depth will be extended from (vector-valued) location parameters to (matrix-valued) dispersion ones.

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