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Title: The influence function of scatter halfspace depth Authors:  Germain Van Bever - Universite de Namur (Belgium) [presenting]
Gaetan Louvet - University de Namur (Belgium)
Abstract: Statistical depth provides robust nonparametric tools to analyze distributions. Depth functions indeed measure the adequacy of distributional parameters to underlying probability measures. In the location case, the celebrated (Tukey) halfspace depth has been widely studied and its robustness properties amply discussed. Recently, depth notions for scatter parameters have been defined and studied. The robustness properties of this latter depth function remain, however, largely unknown. We derive the influence function of scatter halfspace depth. Expressions are given in the known and unknown location case under mild distributional assumptions. In the latter case, the expression allows disentangling the unknown location effect from the scatter contamination. The corresponding asymptotic variance is also provided.