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Simple estimation of the mode of a multivariate density
Author(s) -
Abraham Christophe,
Biau Gérard,
Cadre Benoît
Publication year - 2003
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315901
Subject(s) - multivariate kernel density estimation , kernel density estimation , multivariate statistics , mathematics , statistics , mode (computer interface) , kernel (algebra) , density estimation , variable kernel density estimation , convergence (economics) , rate of convergence , kernel method , computer science , combinatorics , artificial intelligence , economics , economic growth , estimator , support vector machine , computer network , channel (broadcasting) , operating system
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.