On the Estimation of a Support Curve of Indeterminate Sharpness

Peter Hall, Michael Nussbaum and Steven E. Stern

Journal of Multivariate Analysis, 1997, vol. 62, issue 2, 204-232

Abstract: We propose nonparametric methods for estimating the support curve of a bivariate density, when the density decreases at a rate which might vary along the curve. Attention is focused on cases where the rate of decrease is relatively fast, this being the most difficult setting. It demands the use of a relatively large number of bivariate order statistics. By way of comparison, support curve estimation in the context of slow rates of decrease of the density may be addressed using methods that employ only a relatively small number of order statistics at the extremities of the point cloud. In this paper we suggest a new type of estimator, based on projecting onto an axis those data values lying within a thin rectangular strip. Adaptive univariate methods are then applied to the problem of estimating an endpoint of the distribution on the axis. The new method is shown to have theoretically optimal performance in a range of settings. Its numerical properties are explored in a simulation study.

Keywords: convergence; rate; curve; estimation; endpoint; order; statistic; regular; variation; support (search for similar items in EconPapers)
Date: 1997
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (16)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0047-259X(97)91681-X
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:62:y:1997:i:2:p:204-232

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 ().