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 Electronic Journal of Probability > Vol. 11 (2006) > Paper 33 open journal systems 


Weighted uniform consistency of kernel density estimators with general bandwidth sequences

Julia Dony, Free University of Brussels (VUB)
Uwe Einmahl, Free University of Brussels (VUB)


Abstract
Let fn,h be a kernel density estimator of a continuous and bounded d-dimensional density f. Let ψ(t) be a positive continuous function such that ||ψ fβ||∞<∞ for some 0<β<1/2. We are interested in the rate of consistency of such estimators with respect to the weighted sup-norm determined by ψ. This problem has been considered by Gin, Koltchinskii and Zinn (2004) for a deterministic bandwidth hn. We provide ``uniform in h'' versions of some of their results, allowing us to determine the corresponding rates of consistency for kernel density estimators where the bandwidth sequences may depend on the data and/or the location.


Full text: PDF

Pages: 844-859

Published on: September 24, 2006
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Electronic Journal of Probability. ISSN: 1083-6489