AS 307 swMATH ID: 14162 Software Authors: Rousseeuw, Peter J.; Ruts, Ida Description: Algorithm AS 307: Bivariate location depth. he half-space depth of a point θ relative to a bivariate data set {x 1 ,⋯,x n } is given by the smallest number of data points contained in a closed half-plane of which the boundary line passes through θ. A straightforward algorithm for the half-space depth needs O(n 2 ) steps. The simplicial depth of θ relative to {x 1 ,⋯,x n } is given by the number of data triangles Δ(x i ,x j ,x k ) that contain θ; this appears to require O(n 3 ) steps. The algorithm proposed here computes both depths in O(nlogn) time, by combining geometric properties with certain sorting and updating mechanisms. Both types of depth can be used for data description, bivariate confidence regions, p-values, quality indices and control charts. Moreover, the algorithm can be extended to the computation of depth contours and bivariate sign test statistics. Homepage: http://www.jstor.org/stable/2986073?seq=1#page_scan_tab_contents Keywords: bivariate sign tests; data triangles; Fortran 77; algorithm AS 307; half-space depth; simplicial depth Related Software: depth; robustbase; fda (R); Miniball; ABCDepth; ddalpha; R; Expd2d; GitHub; Rainbow; UCI-ml; AS 78; AS 277; Matlab; CompPD; BENSOLVE; Expectreg; aplpack; expdepth; mvShapiroTest Cited in: 61 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Bivariate location depth. Zbl 0905.62002Rousseeuw, Peter J.; Ruts, Ida 1996 all top 5 Cited by 102 Authors 8 Rousseeuw, Peter J. 6 Zuo, Yijun 4 Aloupis, Greg 4 Serfling, Robert J. 3 Hubert, Mia 3 Ruts, Ida 3 Struyf, Anja 3 Wilcox, Rand R. 2 Chaudhuri, Probal 2 Dyckerhoff, Rainer 2 Elmasry, Amr 2 Ghosh, Anil Kumar 2 Langerman, Stefan 2 Liu, Regina Y. C. 2 Liu, Xiaohui 2 Massé, Jean-Claude 2 Mustafa, Nabil Hassan 2 Plante, Jean-François 2 Segaert, Pieter 2 Soss, Michael A. 2 Stephen, Tamon 2 Toussaint, Godfried T. 2 Zasenko, Olga 1 Abellanas, Manuel 1 Baggerly, Keith A. 1 Bazovkin, Pavel 1 Bogićević, Milica 1 Cascos, Ignacio 1 Chakraborty, Biman 1 Chenouri, Shojaeddin 1 Claverol, Mercè 1 Corbellini, Aldo 1 Cortés, Carmen 1 Dai, Yi 1 De Loera, Jesús A. 1 Durocher, Stephane 1 Dutta, Subhajit 1 Eddy, William F. 1 Elbassioni, Khaled M. 1 Fraser, Robert 1 Gągolewski, Marek 1 Gel, Yulia R. 1 Genton, Marc G. 1 Goaoc, Xavier 1 Gomez, Francisco J. 1 Hallin, Marc 1 Hamel, Andreas H. 1 Hering, Franz 1 Hettmansperger, Thomas P. 1 Hlubinka, Daniel 1 Hurtado, Ferran 1 Hwang, Jinsoo 1 Jorn, Hongsuk 1 Kim, Jeankyung 1 Kostner, Daniel 1 Kotík, Lukáš 1 Lai, Shaoyong 1 Lange, Tatjana 1 Leblanc, Alexandre 1 Li, Jun 1 Li, Zhonghua 1 Lin, Juan K. 1 López-Pintado, Sara 1 Makino, Kazuhisa 1 McLeish, Erin 1 Merkle, Milan J. 1 Messaoud, Amor 1 Meunier, Frédéric 1 Morrison, Jason 1 Mosler, Karl Clemens 1 Mozharovskyi, Pavlo 1 Nolan, Deborah 1 Ochoa, Maicol A. 1 Oja, Hannu 1 Paindaveine, Davy 1 Parelius, Jesse M. 1 Pilz, Alexander 1 Rafalin, Eynat 1 Ren, Haiping 1 Riani, Marco 1 Romanazzi, Mario 1 Scott, David W. 1 Šiman, Miroslav 1 Singh, Kesar 1 Skala, Matthew 1 Small, Christopher G. 1 Souvaine, Diane L. 1 Steiger, William L. 1 Sun, Ying 1 Tian, Yahui 1 Tiwary, Hans Raj 1 Van der Veeken, Stephan 1 Vencálek, Ondřej 1 Visuri, Samuli 1 Wang, Guofu 1 Wang, Yunfei 1 Wang, Zhaojun 1 Weihs, Claus 1 Welzl, Emo 1 Werner, Daniel ...and 2 more Authors all top 5 Cited in 28 Serials 15 Computational Statistics and Data Analysis 4 The Annals of Statistics 4 Journal of Multivariate Analysis 3 Advances in Data Analysis and Classification. ADAC 2 Journal of Statistical Planning and Inference 2 Statistics & Probability Letters 2 International Journal of Computational Geometry & Applications 2 Computational Geometry 2 Communications in Statistics. Simulation and Computation 2 Journal of Applied Statistics 1 Information Processing Letters 1 Metrika 1 Annals of the Institute of Statistical Mathematics 1 Fuzzy Sets and Systems 1 Kybernetika 1 Journal of the Royal Statistical Society. Series C 1 Statistical Science 1 Discrete & Computational Geometry 1 Computational Statistics 1 YUJOR. Yugoslav Journal of Operations Research 1 Bulletin of the American Mathematical Society. New Series 1 Bernoulli 1 Theory of Computing Systems 1 Journal of Systems Science and Complexity 1 AStA. Allgemeines Statistisches Archiv 1 Journal of Discrete Algorithms 1 Statistical Methods and Applications 1 Electronic Journal of Statistics all top 5 Cited in 9 Fields 53 Statistics (62-XX) 10 Computer science (68-XX) 9 Numerical analysis (65-XX) 5 Convex and discrete geometry (52-XX) 5 Operations research, mathematical programming (90-XX) 3 Combinatorics (05-XX) 3 Probability theory and stochastic processes (60-XX) 1 Manifolds and cell complexes (57-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Citations by Year