Nonparametric function estimation subject to monotonicity, convexity and other shape constraints
This paper uses free-knot and fixed-knot regression splines in a Bayesian context to develop methods for the nonparametric estimation of functions subject to shape constraints in models with log-concave likelihood functions. The shape constraints we consider include monotonicity, convexity and functions with a single minimum. A computationally efficient MCMC sampling algorithm is developed that converges faster than previous methods for non-Gaussian models. Simulation results indicate the monotonically constrained function estimates have good small sample properties relative to (i)Â unconstrained function estimates, and (ii) function estimates obtained from other constrained estimation methods when such methods exist. Also, asymptotic results show the methodology provides consistent estimates for a large class of smooth functions. Two detailed illustrations exemplify the ideas.
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.
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.:
- Duffie, Darrell & Saita, Leandro & Wang, Ke, 2007.
"Multi-period corporate default prediction with stochastic covariates,"
Journal of Financial Economics,
Elsevier, vol. 83(3), pages 635-665, March.
- Darrel Duffie & Leandro Saita & Ke Wang, 2005. "Multi-Period Corporate Default Prediction With Stochastic Covariates," CIRJE F-Series CIRJE-F-373, CIRJE, Faculty of Economics, University of Tokyo.
- Darrell Duffie & Leandro Siata & Ke Wang, 2006. "Multi-Period Corporate Default Prediction With Stochastic Covariates," NBER Working Papers 11962, National Bureau of Economic Research, Inc.
- Darrel Duffie & Leandro Saita & Ke Wang, 2005. "Multi-Period Corporate Default Prediction With Stochastic Covariates," CARF F-Series CARF-F-047, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
- Yatchew, Adonis & Hardle, Wolfgang, 2006. "Nonparametric state price density estimation using constrained least squares and the bootstrap," Journal of Econometrics, Elsevier, vol. 133(2), pages 579-599, August.
- Charles F. Manski & Elie Tamer, 2002. "Inference on Regressions with Interval Data on a Regressor or Outcome," Econometrica, Econometric Society, vol. 70(2), pages 519-546, March.
- Gallant, A. Ronald, 1981. "On the bias in flexible functional forms and an essentially unbiased form : The fourier flexible form," Journal of Econometrics, Elsevier, vol. 15(2), pages 211-245, February.
- Panagiotelis, Anastasios & Smith, Michael, 2008. "Bayesian identification, selection and estimation of semiparametric functions in high-dimensional additive models," Journal of Econometrics, Elsevier, vol. 143(2), pages 291-316, April.
- 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.
- Christensen, Laurits R & Jorgenson, Dale W & Lau, Lawrence J, 1975. "Transcendental Logarithmic Utility Functions," American Economic Review, American Economic Association, vol. 65(3), pages 367-383, June.
- Banerjee, Moulinath & Mukherjee, Debasri & Mishra, Santosh, 2009. "Semiparametric binary regression models under shape constraints with an application to Indian schooling data," Journal of Econometrics, Elsevier, vol. 149(2), pages 101-117, April.
- Stephen P. Jenkins & Carlos GarcÌa-Serrano, 2004. "The Relationship between Unemployment Benefits and Re-employment Probabilities: Evidence from Spain," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 66(2), pages 239-260, 05.
- Jinyoung Kim & Gerald Marschke, 2005. "Labor Mobility of Scientists, Technological Diffusion, and the Firm's Patenting Decision," RAND Journal of Economics, The RAND Corporation, vol. 36(2), pages 298-317, Summer.
- Gerald Marschke & Jinyoung Kim, 2001. "Labor Mobility of Scientists, Technological Diffusion, and the Firm's Patenting Decision," Discussion Papers 01-03, University at Albany, SUNY, Department of Economics.
- 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.
- Broadie, Mark & Detemple, Jerome & Ghysels, Eric & Torres, Olivier, 2000. "American options with stochastic dividends and volatility: A nonparametric investigation," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 53-92.
- Mark Broadie & Jérôme B. Detemple & Eric Ghysels & Olivier Torrès, 1996. "American Options with Stochastic Dividends and Volatility: A Nonparametric Investigation," CIRANO Working Papers 96s-26, CIRANO.
- Ihara, T. & Genchi, Y. & Sato, T. & Yamaguchi, K. & Endo, Y., 2008. "City-block-scale sensitivity of electricity consumption to air temperature and air humidity in business districts of Tokyo, Japan," Energy, Elsevier, vol. 33(11), pages 1634-1645.
- Pardo, Angel & Meneu, Vicente & Valor, Enric, 2002. "Temperature and seasonality influences on Spanish electricity load," Energy Economics, Elsevier, vol. 24(1), pages 55-70, January.
- Smith, Michael & Kohn, Robert, 1996. "Nonparametric regression using Bayesian variable selection," Journal of Econometrics, Elsevier, vol. 75(2), pages 317-343, December.
- Smith, M. & Kohn, R., "undated". "Nonparametric Regression using Bayesian Variable Selection," Statistics Working Paper _009, Australian Graduate School of Management.
- Barnett, William A. & Serletis, Apostolos, 2008. "Consumer preferences and demand systems," Journal of Econometrics, Elsevier, vol. 147(2), pages 210-224, December.
- William Barnett & Apostolos Serletis, 2008. "Consumer preferences and demand systems," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200801, University of Kansas, Department of Economics, revised Jan 2008.
- Barnett, William A. & Serletis, Apostolos, 2008. "Consumer preferences and demand systems," MPRA Paper 8413, University Library of Munich, Germany.
- Barnett, William A. & Serletis, Apostolos, 2008. "Measuring Consumer Preferences and Estimating Demand Systems," MPRA Paper 12318, University Library of Munich, Germany.
- William Barnett & Apostolos Serletis, 2009. "Measuring Consumer Preferences and Estimating Demand Systems," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200901, University of Kansas, Department of Economics, revised Jan 2009.
- Barnett, William A. & Jonas, Andrew B., 1983. "The Muntz-Szatz demand system : An application of a globally well behaved series expansion," Economics Letters, Elsevier, vol. 11(4), pages 337-342.
- Stephen Walker & Nils Lid Hjort, 2001. "On Bayesian consistency," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(4), pages 811-821.
- Dunson, David B., 2005. "Bayesian Semiparametric Isotonic Regression for Count Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 618-627, June.
- P. Damlen & J. Wakefield & S. Walker, 1999. "Gibbs sampling for Bayesian non-conjugate and hierarchical models by using auxiliary variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 331-344.
- Psiloglou, B.E. & Giannakopoulos, C. & Majithia, S. & Petrakis, M., 2009. "Factors affecting electricity demand in Athens, Greece and London, UK: A comparative assessment," Energy, Elsevier, vol. 34(11), pages 1855-1863.
- Cooper, Russel J & McLaren, Keith R, 1996. "A System of Demand Equations Satisfying Effectively Global Regularity Conditions," The Review of Economics and Statistics, MIT Press, vol. 78(2), pages 359-364, May.
- Smith, M. & Wong, C.M. & Kohn, R., 1996. "Additive Nonparametric Regression with Autocorrelated Errors," Monash Econometrics and Business Statistics Working Papers 19/96, Monash University, Department of Econometrics and Business Statistics.
- Broadie, Mark & Detemple, Jerome & Ghysels, Eric & Torres, Olivier, 2000. "Nonparametric estimation of American options' exercise boundaries and call prices," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1829-1857, October.
- Mark Broadie & Jérôme B. Detemple & Eric Ghysels & Olivier Torrès, 1996. "Nonparametric Estimation of American Options Exercise Boundaries and Call Prices," CIRANO Working Papers 96s-24, CIRANO.
- Jaap H. Abbring & Gerard J. van den Berg, 2003. "The Nonparametric Identification of Treatment Effects in Duration Models," Econometrica, Econometric Society, vol. 71(5), pages 1491-1517, 09.
- Sreedhar T. Bharath & Tyler Shumway, 2008. "Forecasting Default with the Merton Distance to Default Model," Review of Financial Studies, Society for Financial Studies, vol. 21(3), pages 1339-1369, May. Full references (including those not matched with items on IDEAS)
When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:161:y:2011:i:2:p:166-181. 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.