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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/4029

Title: Modifying the kernel distribution function estimator towards reduced bias
Authors: JANSSEN, Paul
Issue Date: 2007
Citation: STATISTICS, 41(2). p. 93-103
Abstract: We explore the convergence rates of a kernel-based distribution function estimator with variable bandwidth. As in density estimation, a considerable bias reduction from O(h(2)) to O(h(4)) can be obtained by replacing the bandwidth h by h/f(1/2)(X-i). We show that the necessary replacement of f(1/2) by some pilot estimator (f) over cap (1/2)(g), depending on a secondbandwidth g, has nopenalizing effect onbias andvariance, provided we undersmooth with the pilot bandwidth g, that is g/h -> 0 in a certain way. Owing to the considerable bias reduction, a simple plug-in normal reference bandwidth selector works effectively in practice. Distribution function estimators with good convergence properties and with simple bandwidth selectors are desirable for repetitive use in smoothed bootstrap algorithms.
Notes: Univ Hasselt, B-3590 Diepenbeek, Belgium. North West Univ, Potchefstroom, South Africa.Veraberbeke, N, Univ Hasselt, Gebouw D, B-3590 Diepenbeek, Belgium.noel.veraverbeke@uhasselt.be
URI: http://hdl.handle.net/1942/4029
DOI: 10.1080/02331880601106561
ISI #: 000245985300001
ISSN: 0233-1888
Category: A1
Type: Journal Contribution
Validation: ecoom, 2008
Appears in Collections: Research publications

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