Estimating a Convex Function in Nonparametric Regression
AbstractA new nonparametric estimate of a convex regression function is proposed and its stochastic properties are studied. The method starts with an unconstrained estimate of the derivative of the regression function, which is firstly isotonized and then integrated. We prove asymptotic normality of the new estimate and show that it is first order asymptotically equivalent to the initial unconstrained estimate if the regression function is in fact convex. If convexity is not present, the method estimates a convex function whose derivative has the same "L"-super-"p"-norm as the derivative of the (non-convex) underlying regression function. The finite sample properties of the new estimate are investigated by means of a simulation study and it is compared with a least squares approach of convex estimation. The application of the new method is demonstrated in two data examples. Copyright 2007 Board of the Foundation of the Scandinavian Journal of Statistics..
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 Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association in its journal Scandinavian Journal of Statistics.
Volume (Year): 34 (2007)
Issue (Month): 2 ()
Contact details of provider:
Web page: http://www.blackwellpublishing.com/journal.asp?ref=0303-6898
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- Samantha Leorato, 2008.
"A refined Jensen’s inequality in Hilbert spaces and empirical approximations,"
CEIS Research Paper
134, Tor Vergata University, CEIS, revised 24 Nov 2008.
- Leorato, S., 2009. "A refined Jensen's inequality in Hilbert spaces and empirical approximations," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 1044-1060, May.
- Dentcheva, Darinka & Penev, Spiridon, 2010. "Shape-restricted inference for Lorenz curves using duality theory," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 403-412, March.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wiley-Blackwell Digital Licensing) or (Christopher F. Baum).
If references are entirely missing, you can add them using this form.