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.
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Volume (Year): 56 (2012)
Issue (Month): 9 ()
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References listed on IDEAS
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- A. Ronald Gallant & Gene H. Golub, 1982.
"Imposing Curvature Restrictions on Flexible Functional Forms,"
538, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- 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.
- 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.
- 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.
- 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.
- 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.
- Chak, Pok Man & Madras, Neal & Smith, Barry, 2005. "Semi-nonparametric estimation with Bernstein polynomials," Economics Letters, Elsevier, vol. 89(2), pages 153-156, November.
- 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.
- 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.
- 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.
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