A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is `application/pdf`

.

##
###
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