Methods for tracking support boundaries with corners
In a range of practical problems the boundary of the support of a bivariate distribution is of interest, for example where it describes a limit to efficiency or performance, or where it determines the physical extremities of a spatially distributed population in forestry, marine science, medicine, meteorology or geology. We suggest a tracking-based method for estimating a support boundary when it is composed of a finite number of smooth curves, meeting together at corners. The smooth parts of the boundary are assumed to have continuously turning tangents and bounded curvature, and the corners are not allowed to be infinitely sharp; that is, the angle between the two tangents should not equal [pi]. In other respects, however, the boundary may be quite general. In particular it need not be uniquely defined in Cartesian coordinates, its corners my be either concave or convex, and its smooth parts may be neither concave nor convex. Tracking methods are well suited to such generalities, and they also have the advantage of requiring relatively small amounts of computation. It is shown that they achieve optimal convergence rates, in the sense of uniform approximation.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 97 (2006)
Issue (Month): 8 (September)
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description|
|Order Information:|| Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Hardle, W. & Park, B. U. & Tsybakov, A. B., 1995. "Estimation of Non-sharp Support Boundaries," Journal of Multivariate Analysis, Elsevier, vol. 55(2), pages 205-218, November.
- Hall, Peter & Park, Byeong U. & Stern, Steven E., 1998. "On Polynomial Estimators of Frontiers and Boundaries," Journal of Multivariate Analysis, Elsevier, vol. 66(1), pages 71-98, July.
- Aigner, Dennis & Lovell, C. A. Knox & Schmidt, Peter, 1977. "Formulation and estimation of stochastic frontier production function models," Journal of Econometrics, Elsevier, vol. 6(1), pages 21-37, July.
- Kneip, Alois & Park, Byeong U. & Simar, L opold, 1998. "A Note On The Convergence Of Nonparametric Dea Estimators For Production Efficiency Scores," Econometric Theory, Cambridge University Press, vol. 14(06), pages 783-793, December.
- PARK, Beyong U. & SICKLES, Robin C. & SIMAR, Léopold, .
"Stochastic panel frontiers: A semiparametric approach,"
CORE Discussion Papers RP
1330, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Park, B. U. & Sickles, R. C. & Simar, L., 1998. "Stochastic panel frontiers: A semiparametric approach," Journal of Econometrics, Elsevier, vol. 84(2), pages 273-301, June.
- PARK, Byeong U. & SICKLES, Robin C. & SIMAR, Léopold, 1996. "Stochastic Panel Frontiers : A Semiparametric Approach," CORE Discussion Papers 1996038, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Peter Hall & Liang Peng & Christian Rau, 2001. "Local likelihood tracking of fault lines and boundaries," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(3), pages 569-582.
- Muller, H. G. & Song, K. S., 1994. "Maximin Estimation of Multidimensional Boundaries," Journal of Multivariate Analysis, Elsevier, vol. 50(2), pages 265-281, August.
- Kneip, A. & Simar, L., .
"A general framework for frontier estimation with panel data,"
CORE Discussion Papers RP
1224, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- KNEIP, Alois & SIMAR, Léopold, 1995. "A General Framework for Frontier Estimation with Panel Data," CORE Discussion Papers 1995060, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Hall, Peter & Nussbaum, Michael & Stern, Steven E., 1997. "On the Estimation of a Support Curve of Indeterminate Sharpness," Journal of Multivariate Analysis, Elsevier, vol. 62(2), pages 204-232, August.
- Tsybakov, A.B. & Korostelev, A.P. & Simar, L., 1992. "Efficient Estimation of Monotone Boundaries," Papers 9209, Catholique de Louvain - Institut de statistique.
When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:97:y:2006:i:8:p:1870-1893. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Shamier, Wendy)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.