Open Access
December 2002 On depth and deep points: a calculus
Ivan Mizera
Ann. Statist. 30(6): 1681-1736 (December 2002). DOI: 10.1214/aos/1043351254


For a general definition of depth in data analysis a differential-like calculus is constructed in which the location case (the framework of Tukey's median) plays a fundamental role similar to that of linear functions in the mathematical analysis. As an application, a lower bound for maximal regression depth is proved in the general multidimensional case--as conjectured by Rousseeuw and Hubert and others. This lower bound is demonstrated to have an impact on the breakdown point of the maximum depth estimator.


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Ivan Mizera. "On depth and deep points: a calculus." Ann. Statist. 30 (6) 1681 - 1736, December 2002.


Published: December 2002
First available in Project Euclid: 23 January 2003

zbMATH: 1039.62046
MathSciNet: MR1969447
Digital Object Identifier: 10.1214/aos/1043351254

Primary: 62H05
Secondary: 52A40 , ‎54C60‎ , 55M25 , 90C29

Keywords: Centerpoint , compactification , degree of mapping , depth , halfspace , Kronecker index , median , multivariate location , regression , set-valued analysis , vector optimization , weak convergence

Rights: Copyright © 2002 Institute of Mathematical Statistics

Vol.30 • No. 6 • December 2002
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