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Title: | Modifying the kernel distribution function estimator towards reduced bias | Authors: | JANSSEN, Paul SWANEPOEL, Jan VERAVERBEKE, Noel |
Issue Date: | 2007 | Publisher: | TAYLOR & FRANCIS LTD | Source: | 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 | Keywords: | bandwidth; bias; distribution function estimator; kernel estimation; mean integrated squared error; smoothed bootstrap | Document URI: | http://hdl.handle.net/1942/4029 | ISSN: | 0233-1888 | e-ISSN: | 1029-4910 | DOI: | 10.1080/02331880601106561 | ISI #: | 000245985300001 | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2008 |
Appears in Collections: | Research publications |
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