Simple estimation of the mode of a multivariate density
The authors consider an estimate of the mode of a multivariate probability density using a kernel estimate drawn from a random sample. The estimate is defined by maximizing the kernel estimate over the set of sample values. The authors show that this estimate is strongly consistent and give an almos...
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| Veröffentlicht in: | Canadian journal of statistics 2003-03, Vol.31 (1), p.23-34 |
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| container_end_page | 34 |
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| container_title | Canadian journal of statistics |
| container_volume | 31 |
| creator | Abraham, Christophe Biau, Gérard Cadre, Benoît |
| description | The authors consider an estimate of the mode of a multivariate probability density using a kernel estimate drawn from a random sample. The estimate is defined by maximizing the kernel estimate over the set of sample values. The authors show that this estimate is strongly consistent and give an almost sure rate of convergence. This rate depends on the sharpness of the density near the true mode, which is measured by a peak index. /// Les auteurs proposent un estimateur du mode d'une densité de probabilité multivariée construit à partir d'un estimateur à noyau basé sur un échantillon aléatoire. Cet estimateur est défini en maximisant l'estimateur à noyau sur les valeurs de l'échantillon. Les auteurs montrent que l'estimateur est fortement convergent et donnent une vitesse de convergence presque sûre. Cette vitesse dépend de la forme de la densité au voisinage du vrai mode, mesurée par un indice de pic. |
| doi_str_mv | 10.2307/3315901 |
| format | Article |
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The estimate is defined by maximizing the kernel estimate over the set of sample values. The authors show that this estimate is strongly consistent and give an almost sure rate of convergence. This rate depends on the sharpness of the density near the true mode, which is measured by a peak index. /// Les auteurs proposent un estimateur du mode d'une densité de probabilité multivariée construit à partir d'un estimateur à noyau basé sur un échantillon aléatoire. Cet estimateur est défini en maximisant l'estimateur à noyau sur les valeurs de l'échantillon. Les auteurs montrent que l'estimateur est fortement convergent et donnent une vitesse de convergence presque sûre. 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The estimate is defined by maximizing the kernel estimate over the set of sample values. The authors show that this estimate is strongly consistent and give an almost sure rate of convergence. This rate depends on the sharpness of the density near the true mode, which is measured by a peak index. /// Les auteurs proposent un estimateur du mode d'une densité de probabilité multivariée construit à partir d'un estimateur à noyau basé sur un échantillon aléatoire. Cet estimateur est défini en maximisant l'estimateur à noyau sur les valeurs de l'échantillon. Les auteurs montrent que l'estimateur est fortement convergent et donnent une vitesse de convergence presque sûre. Cette vitesse dépend de la forme de la densité au voisinage du vrai mode, mesurée par un indice de pic.</abstract><cop>Hoboken</cop><pub>Wiley-Blackwell</pub><doi>10.2307/3315901</doi><tpages>12</tpages></addata></record> |
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| ispartof | Canadian journal of statistics, 2003-03, Vol.31 (1), p.23-34 |
| issn | 0319-5724 1708-945X |
| language | eng |
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| source | JSTOR Mathematics & Statistics; Access via Wiley Online Library; JSTOR Archive Collection A-Z Listing |
| subjects | Cluster analysis Consistent estimators Convergence Density Density estimation Estimation Kernel estimate Logical proofs Mathematical methods Mode Model testing multivariate probability density Nomographs Probabilities Probability rate of convergence Real numbers Statistical methods Statistical mode Statistics |
| title | Simple estimation of the mode of a multivariate density |
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