IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this article or follow this journal

Nonparametric function estimation subject to monotonicity, convexity and other shape constraints

  • Shively, Thomas S.
  • Walker, Stephen G.
  • Damien, Paul
Registered author(s):

    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.

    File URL: http://www.sciencedirect.com/science/article/B6VC0-51S0WYJ-1/2/ca9d256cd29ef36743638270d39b9c49
    Download Restriction: Full text for ScienceDirect subscribers only

    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.

    Article provided by Elsevier in its journal Journal of Econometrics.

    Volume (Year): 161 (2011)
    Issue (Month): 2 (April)
    Pages: 166-181

    as
    in new window

    Handle: RePEc:eee:econom:v:161:y:2011:i:2:p:166-181
    Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

    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.:

    as in new window
    1. Barnett, William A. & Serletis, Apostolos, 2008. "Consumer preferences and demand systems," MPRA Paper 8413, University Library of Munich, Germany.
    2. 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.
    3. Smith, Michael & Kohn, Robert, 1996. "Nonparametric regression using Bayesian variable selection," Journal of Econometrics, Elsevier, vol. 75(2), pages 317-343, December.
    4. 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.
    5. 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.
    6. 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.
    7. Christensen, Laurits R & Jorgenson, Dale W & Lau, Lawrence J, 1975. "Transcendental Logarithmic Utility Functions," American Economic Review, American Economic Association, vol. 65(3), pages 367-83, June.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Yacine Ait-Sahalia & Jefferson Duarte, 2002. "Nonparametric Option Pricing under Shape Restrictions," NBER Working Papers 8944, National Bureau of Economic Research, Inc.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. 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 359-64, May.
    21. 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.
    22. 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.
    23. 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.
    24. 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.
    25. 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.
    26. 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.
    Full references (including those not matched with items on IDEAS)

    This item is not listed on Wikipedia, on a reading list or among the top 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: (Zhang, Lei)

    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.

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.