Shape restricted nonparametric regression with Bernstein polynomials
The objective of this article is to develop a computationally efficient estimator of the regression function subject to various shape constraints. In particular, nonparametric estimators of monotone and/or convex (concave) regression functions are obtained by using a nested sequence of Bernstein polynomials. One of the key distinguishing features of the proposed estimator is that a given shape constraint (e.g., monotonicity and/or convexity) is maintained for any finite sample size and satisfied over the entire support of the predictor space. Moreover, it is shown that the Bernstein polynomial based regression estimator can be obtained as a solution of a constrained least squares method and hence the estimator can be computed efficiently using a quadratic programming algorithm. Finally, the asymptotic properties (e.g., strong uniform consistency) of the estimator are established under very mild conditions, and finite sample properties are explored using several simulation studies and real data analysis. The predictive performances are compared with some of the existing methods.
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): 56 (2012)
Issue (Month): 9 ()
|Contact details of provider:|| Web page: http://www.elsevier.com/locate/csda|
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.:
- S. McKay Curtis & Sujit K. Ghosh, 2011. "A variable selection approach to monotonic regression with Bernstein polynomials," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(5), pages 961-976, February.
- Bornkamp, BjÃ¶rn & Ickstadt, Katja, 2009. "A Note on B-Splines for Semiparametric Elicitation," The American Statistician, American Statistical Association, vol. 63(4), pages 373-377.
- I-Shou Chang & Chao A. Hsiung & Yuh-Jenn Wu & Che-Chi Yang, 2005. "Bayesian Survival Analysis Using Bernstein Polynomials," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(3), pages 447-466.
- Ait-Sahalia, Yacine & Duarte, Jefferson, 2003.
"Nonparametric option pricing under shape restrictions,"
Journal of Econometrics,
Elsevier, vol. 116(1-2), pages 9-47.
- Yacine Ait-Sahalia & Jefferson Duarte, 2002. "Nonparametric Option Pricing under Shape Restrictions," NBER Working Papers 8944, National Bureau of Economic Research, Inc.
- Chak, Pok Man & Madras, Neal & Smith, Barry, 2005. "Semi-nonparametric estimation with Bernstein polynomials," Economics Letters, Elsevier, vol. 89(2), pages 153-156, November.
- Gallant, A. Ronald & Golub, Gene H., 1984.
"Imposing curvature restrictions on flexible functional forms,"
Journal of Econometrics,
Elsevier, vol. 26(3), pages 295-321, December.
- A. Ronald Gallant & Gene H. Golub, 1982. "Imposing Curvature Restrictions on Flexible Functional Forms," Discussion Papers 538, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Terrell, Dek, 1996. "Incorporating Monotonicity and Concavity Conditions in Flexible Functional Forms," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(2), pages 179-194, March-Apr.
- Sonia Petrone, 1999. "Random Bernstein Polynomials," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(3), pages 373-393.
- Melanie Birke & Holger Dette, 2007. "Estimating a Convex Function in Nonparametric Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(2), pages 384-404.
When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:56:y:2012:i:9:p:2729-2741. 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: (Dana Niculescu)
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.