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On the asymptotic properties of a simple estimate of the Mode
2004
E S A I M: Probability & Statistics
We consider an estimate of the mode θ of a multivariate probability density f with support in R d using a kernel estimate fn drawn from a sample X1, . . . , Xn. The estimate θn is defined as any x in {X1, . . . , Xn} such that fn(x) = maxi=1,...,n fn(Xi). It is shown that θn behaves asymptotically as any maximizerθn of fn. More precisely, we prove that for any sequence (rn) n≥1 of positive real numbers such that rn → ∞ and r d n log n/n → 0, one has rn θn −θn → 0 in probability. The asymptotic
doi:10.1051/ps:2003015
fatcat:xjz4d4fotrdyfawmlrdbnrx4yq