The quarter median

Ludwig Baringhaus () and Rudolf Grübel ()
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Ludwig Baringhaus: Leibniz Universität Hannover
Rudolf Grübel: Leibniz Universität Hannover

Metrika: International Journal for Theoretical and Applied Statistics, 2022, vol. 85, issue 4, No 2, 419-458

Abstract: Abstract 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.

Keywords: Asymptotic normality; Consistency; Estimation of location; Euclidean motion equivariance; Equipartition; Multivariate median; 62H12; 62H11; 62F35 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s00184-021-00836-z

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