Lower bounds for computing statistical depth
Given 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 a...
| Autores: | , , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2002 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/163675 |
| Acceso en línea: | https://hdl.handle.net/11441/163675 https://doi.org/10.1016/S0167-9473(02)00032-4 |
| Access Level: | acceso abierto |
| Palabra clave: | Simplicial depth Halfspace depth Liu Tukey Sign tests |
| Sumario: | Given 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. |
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