A0373
Title: Data depth for probability measures
Authors: Myriam Vimond - ENSAI (France) [presenting]
Pavlo Mozharovskyi - Telecom Paris, Institut Polytechnique de Paris (France)
Pierre Lafaye de Micheaux - UNSW Sydney (Australia)
Abstract: Statistical data depth measures the centrality of a given point in space with respect to a finite sample or with respect to a probability measure in that space. Over the last few decades, this seminal idea of data depth has evolved into a powerful tool that has proven useful in various fields of science. Recently, the notion of data depth was extended to unparametrized curves. A notion of data depth is proposed, which is suitable for data represented as probability measures. Applications with finite finite point processes are considered, with distributions of random closed sets, or with models of germ grain coverage. Depending on the geometry of the data, adaptations of this depth are investigated, for example, by introducing a weight. It is shown that the depth satisfies the theoretical requirements of general depth functions that are meaningful for applications.
