2024-10-152024-10-152002Aloupis, G., Cortés Parejo, M.d.C., Gomez, F., Soss, M. y Toussaint, G. (2002). Lower bounds for computing statistical depth. Computational statistics & data analysis, 40 (2), 223-229. https://doi.org/10.1016/S0167-9473(02)00032-4.0167-94731872-7352https://hdl.handle.net/11441/163675Given a 0nite set of points S, two measures of the depth of a query point with respect to S are the Simplicial depth of Liu andthe Halfspace depth of Tukey (also known as Location depth). We show that computing these depths requires 4(n log n) time, which matches the upper boundcomplexities of the algorithms of Rousseeuw andRuts. Our lower boundproofs may also be appliedto two bivariate sign tests: that of Hodges, andthat of Oja and Nyblom.application/pdf7 p.engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Simplicial depthHalfspace depthLiuTukeySign testsinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess10.1016/S0167-9473(02)00032-4