Document Type
Article
Publication Date
4-1-2003
Publication Title
Statistics and Computing
Abstract
The concept of location depth was introduced as a way to extend the univariate notion of ranking to a bivariate configuration of data points. It has been used successfully for robust estimation, hypothesis testing, and graphical display. The depth contours form a collection of nested polygons, and the center of the deepest contour is called the Tukey median. The only available implemented algorithms for the depth contours and the Tukey median are slow, which limits their usefulness. In this paper we describe an optimal algorithm which computes all bivariate depth contours in O(n 2) time and space, using topological sweep of the dual arrangement of lines. Once these contours are known, the location depth of any point can be computed in O(log 2 n) time with no additional preprocessing or in O(log n) time after O(n 2) preprocessing. We provide fast implementations of these algorithms to allow their use in everyday statistical practice.
Keywords
Bagplot, Bivariate median, Graphical display, Robust estimation, Tukey depth
Volume
13
Issue
2
First Page
153
Last Page
162
DOI
10.1023/A:1023208625954
ISSN
09603174
Recommended Citation
Miller, Kim; Ramaswami, Suneeta; Rousseeuw, Peter; Antoni Sellarès, J.; Souvaine, Diane; Streinu, Ileana; and Struyf, Anja, "Efficient Computation of Location Depth Contours by Methods of Computational Geometry" (2003). Computer Science: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/csc_facpubs/291
Comments
Archived as published.