Halfplane trimming for bivariate distributions
Journal of Multivariate Analysis
Computing depth contours of bivariate point clouds
Computational Statistics & Data Analysis - Special issue on classification
Statistical Models in S
Efficient algorithms for maximum regression depth
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Proceedings of the sixteenth annual symposium on Computational geometry
Fast implementation of depth contours using topological sweep
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Journal of Multivariate Analysis
A Monte Carlo study of the accuracy and robustness of ten bivariate location estimators
Computational Statistics & Data Analysis
Deterministic sampling and range counting in geometric data streams
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Deterministic sampling and range counting in geometric data streams
ACM Transactions on Algorithms (TALG)
Computing zonoid trimmed regions of dimension d2
Computational Statistics & Data Analysis
Robust classification for skewed data
Advances in Data Analysis and Classification
Selecting training points for one-class support vector machines
Pattern Recognition Letters
Measuring overlap in binary regression
Computational Statistics & Data Analysis
The Depth Problem: Identifying the Most Representative Units in a Data Group
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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The location depth (Tukey 1975) of a point θ relative to a p-dimensional data set Z of size n is defined as the smallest number of data points in a closed halfspace with boundary through θ. For bivariate data, it can be computed in O(nlogn) time (Rousseeuw and Ruts 1996). In this paper we construct an exact algorithm to compute the location depth in three dimensions in O(n2logn) time. We also give an approximate algorithm to compute the location depth in p dimensions in O(mp3+mpn) time, where m is the number of p-subsets used.Recently, Rousseeuw and Hubert (1996) defined the depth of a regression fit. The depth of a hyperplane with coefficients (θ1,…,θp) is the smallest number of residuals that need to change sign to make (θ1,…,θp) a nonfit. For bivariate data (p=2) this depth can be computed in O(nlogn) time as well. We construct an algorithm to compute the regression depth of a plane relative to a three-dimensional data set in O(n2logn) time, and another that deals with p=4 in O(n3logn) time. For data sets with large n and/or p we propose an approximate algorithm that computes the depth of a regression fit in O(mp3+mpn+mnlogn) time. For all of these algorithms, actual implementations are made available.