Bandwidth choice for local polynomial estimation of smooth boundaries

Peter Hall and Byeong U. Park

Journal of Multivariate Analysis, 2004, vol. 91, issue 2, 240-261

Abstract: Local polynomial methods hold considerable promise for boundary estimation, where they offer unmatched flexibility and adaptivity. Most rival techniques provide only a single order of approximation; local polynomial approaches allow any order desired. Their more conventional rivals, for example high-order kernel methods in the context of regression, do not have attractive versions in the case of boundary estimation. However, the adoption of local polynomial methods for boundary estimation is inhibited by lack of knowledge about their properties, in particular about the manner in which they are influenced by bandwidth; and by the absence of techniques for empirical bandwidth choice. In the present paper we detail the way in which bandwidth selection determines mean squared error of local polynomial boundary estimators, showing that it is substantially more complex than in regression settings. For example, asymptotic formulae for bias and variance contributions to mean squared error no longer decompose into monotone functions of bandwidth. Nevertheless, once these properties are understood, relatively simple empirical bandwidth selection methods can be developed. We suggest a new approach to both local and global bandwidth choice, and describe its properties.

Keywords: Bandwidth; choice; Bootstrap; Global; bandwidth; Local; bandwidth; Local; polynomial; methods; Nonparametric; curve; estimation (search for similar items in EconPapers)
Date: 2004
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (10)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0047-259X(03)00177-5
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:91:y:2004:i:2:p:240-261

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().