×

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); ABCDepth; ddalpha; R; Expd2d; GitHub; Rainbow; UCI-ml; AS 78; AS 277; Matlab; CompPD; BENSOLVE; aplpack; expdepth; Expectreg; mvShapiroTest; CRAN
Referenced in: 61 Publications

Standard Articles

1 Publication describing the Software, including 1 Publication in zbMATH Year
Bivariate location depth. Zbl 0905.62002
Rousseeuw, Peter J.; Ruts, Ida
1996
all top 5

Referenced 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

Referencing Publications by Year