 Rates of convergence for the pre-asymptotic substitution bandwidth selectorJianqing Fan and Li-Shan Huang Statistics & Probability Letters, 1999, vol. 43, issue 3, 309-316 Abstract: An effective bandwidth selection method for local linear regression is proposed in Fan and Gijbels [1995, J. Roy. Statist. Soc. Ser. B, 57, 371-394]. The method is based on the idea of the pre-asymptotic substitution and has been tested extensively. This paper investigates the rate of convergence of this method. In particular, we show that the relative rate of convergence is of order n-2/7 if the locally cubic fitting is used in the pilot stage, and the rate of convergence is n-2/5 when the local polynomial of degree 5 is used in the pilot fitting. The study also reveals a marked difference between the bandwidth selection for nonparametric regression and that for density estimation: The plug-in approach for the latter case can admit the root-n rate of convergence while for the former case the best rate is of order n-2/5. Keywords: Bandwidth; selection; Convergence; rate; Local; polynomial; regression; Kernel; density; estimation (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:43:y:1999:i:3:p:309-316 Ordering information: This journal article can be ordered from Access Statistics for this article Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul More articles in Statistics & Probability Letters from Elsevier |
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