Maximin Estimation of Multidimensional Boundaries
AbstractWe consider the problem of estimating the location and size of a discontinuity in an otherwise smooth multidimensional regression function. The boundary or location of the discontinuity is assumed to be a closed curve respective surface, and we aim to estimate this closed set. Our approach utilizes the uniform convergence of multivariate kernel estimators for directional limits. Differences of such limits converge to zero under smoothness assumptions, and to the jump size along the discontinuity. This leads to the proposal of a maximin estimator, which selects the boundary for which the minimal estimated directional difference among all points belonging to this boundary is maximized. It is shown that this estimated boundary is almost surely enclosed in a sequence of shrinking neighborhoods around the true boundary, and corresponding rates of convergence are obtained.
Download InfoIf 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.
Bibliographic InfoArticle provided by Elsevier in its journal Journal of Multivariate Analysis.
Volume (Year): 50 (1994)
Issue (Month): 2 (August)
Contact details of provider:
Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- Cheng, Ming-Yen & Hall, Peter, 2006. "Methods for tracking support boundaries with corners," Journal of Multivariate Analysis, Elsevier, vol. 97(8), pages 1870-1893, September.
- Delgado, Miguel A. & Hidalgo, Javier, 2000. "Nonparametric inference on structural breaks," Journal of Econometrics, Elsevier, vol. 96(1), pages 113-144, May.
- Garlipp, T. & Muller, C.H., 2006. "Detection of linear and circular shapes in image analysis," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1479-1490, December.
- Polzehl, Jörg & Spokojnyj, Vladimir G., 1998. "Image denoising: Pointwise adaptive approach," SFB 373 Discussion Papers 1998,38, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- Peihua Qiu, 2009. "Jump-preserving surface reconstruction from noisy data," Annals of the Institute of Statistical Mathematics, Springer, vol. 61(3), pages 715-751, September.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
If references are entirely missing, you can add them using this form.