The Annals of Statistics
- Ann. Statist.
- Volume 30, Number 6 (2002), 1681-1736.
On depth and deep points: a calculus
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.
Ann. Statist., Volume 30, Number 6 (2002), 1681-1736.
First available in Project Euclid: 23 January 2003
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62H05: Characterization and structure theory
Secondary: 52A40: Inequalities and extremum problems 54C60: Set-valued maps [See also 26E25, 28B20, 47H04, 58C06] 55M25: Degree, winding number 90C29: Multi-objective and goal programming
Mizera, Ivan. On depth and deep points: a calculus. Ann. Statist. 30 (2002), no. 6, 1681--1736. doi:10.1214/aos/1043351254. https://projecteuclid.org/euclid.aos/1043351254