On the asymptotic properties of a simple estimate of the Mode
Christophe Abraham, Gérard Biau, Benoît Cadre (2010)
ESAIM: Probability and Statistics
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We consider an estimate of the mode of a multivariate probability density with support in using a kernel estimate drawn from a sample . The estimate is defined as any in {} such that . It is shown that behaves asymptotically as any maximizer of . More precisely, we prove that for any sequence of positive real numbers such that and , one has in probability. The asymptotic normality of follows without further work.