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The quarter median. (English) Zbl 1493.62296

Summary: We introduce and discuss a multivariate version of the classical median that is based on an equipartition property with respect to quarter spaces. These arise as pairwise intersections of the half-spaces associated with the coordinate hyperplanes of an orthogonal basis. We obtain results on existence, equivariance, and asymptotic normality.

MSC:

62H12 Estimation in multivariate analysis
62H11 Directional data; spatial statistics
62F35 Robustness and adaptive procedures (parametric inference)
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