IDEAS home Printed from
   My bibliography  Save this article

Semi-Nonparametric Interval-Censored Mixed Proportional Hazard Models: Identification And Consistency Results


  • Bierens, Herman J.


In this paper I propose estimating distributions on the unit interval semi-nonparametrically using orthonormal Legendre polynomials. This approach will be applied to the interval-censored mixed proportional hazard (ICMPH) model, where the distribution of the unobserved heterogeneity is modeled semi-nonparametrically. Various conditions for the nonparametric identification of the ICMPH model are derived. I will prove general consistency results for M -estimators of (partly) non-euclidean parameters under weak and easy-to-verify conditions and specialize these results to sieve estimators. Special attention is paid to the case where the support of the covariates is finite.

Suggested Citation

  • Bierens, Herman J., 2008. "Semi-Nonparametric Interval-Censored Mixed Proportional Hazard Models: Identification And Consistency Results," Econometric Theory, Cambridge University Press, vol. 24(03), pages 749-794, June.
  • Handle: RePEc:cup:etheor:v:24:y:2008:i:03:p:749-794_08

    Download full text from publisher

    File URL:
    File Function: link to article abstract page
    Download Restriction: no

    References listed on IDEAS

    1. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643, March.
    2. Susanne M. Schennach, 2004. "Estimation of Nonlinear Models with Measurement Error," Econometrica, Econometric Society, vol. 72(1), pages 33-75, January.
    3. Lu, Zhan-Qian, 1999. "Nonparametric Regression with Singular Design," Journal of Multivariate Analysis, Elsevier, vol. 70(2), pages 177-201, August.
    4. Green, David A & Riddell, W Craig, 1997. "Qualifying for Unemployment Insurance: An Empirical Analysis," Economic Journal, Royal Economic Society, vol. 107(440), pages 67-84, January.
    5. Li, Qi & Racine, Jeff, 2003. "Nonparametric estimation of distributions with categorical and continuous data," Journal of Multivariate Analysis, Elsevier, vol. 86(2), pages 266-292, August.
    6. Phillips, Peter C.B., 1995. "Robust Nonstationary Regression," Econometric Theory, Cambridge University Press, vol. 11(05), pages 912-951, October.
    7. Frigyesi, Attila & Hössjer, Ola, 1998. "A test for singularity," Statistics & Probability Letters, Elsevier, vol. 40(3), pages 215-226, October.
    8. Victoria Zinde-Walsh & Peter C.B. Phillips, 2003. "Fractional Brownian Motion as a Differentiable Generalized Gaussian Process," Cowles Foundation Discussion Papers 1391, Cowles Foundation for Research in Economics, Yale University.
    9. Zinde-Walsh, Victoria, 2002. "Asymptotic Theory For Some High Breakdown Point Estimators," Econometric Theory, Cambridge University Press, vol. 18(05), pages 1172-1196, October.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Arulampalam, Wiji & Corradi, Valentina & Gutknecht, Daniel, 2014. "Modelling Heaped Duration Data: An Application to Neonatal Mortality," CAGE Online Working Paper Series 207, Competitive Advantage in the Global Economy (CAGE).
    2. repec:eee:transb:v:106:y:2017:i:c:p:173-192 is not listed on IDEAS
    3. Herman J. Bierens & Jose R. Carvalho, 2007. "Semi-nonparametric competing risks analysis of recidivism," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(5), pages 971-993.
    4. Fosgerau, Mogens & Mabit, Stefan L., 2013. "Easy and flexible mixture distributions," Economics Letters, Elsevier, vol. 120(2), pages 206-210.
    5. Mogens Fosgerau, 2014. "Nonparametric approaches to describing heterogeneity," Chapters,in: Handbook of Choice Modelling, chapter 11, pages 257-267 Edward Elgar Publishing.
    6. Christian N. Brinch, 2008. "Non-parametric Identification of the Mixed Hazards Model with Interval-Censored Durations," Discussion Papers 539, Statistics Norway, Research Department.
    7. Fosgerau, Mogens & Hess, Stephane, 2008. "Competing methods for representing random taste heterogeneity in discrete choice models," MPRA Paper 10038, University Library of Munich, Germany.
    8. Fosgerau, Mogens & Hess, Stephane, 2009. "A comparison of methods for representing random taste heterogeneity in discrete choice models," European Transport \ Trasporti Europei, ISTIEE, Institute for the Study of Transport within the European Economic Integration, issue 42, pages 1-25.
    9. Fosgerau, Mogens & Hjort, Katrine & Vincent Lyk-Jensen, Stéphanie, 2007. "An approach to the estimation of the distribution of marginal valuations from discrete choice data," MPRA Paper 3907, University Library of Munich, Germany.
    10. Bierens, Herman J. & Song, Hosin, 2012. "Semi-nonparametric estimation of independently and identically repeated first-price auctions via an integrated simulated moments method," Journal of Econometrics, Elsevier, vol. 168(1), pages 108-119.
    11. repec:eee:econom:v:200:y:2017:i:2:p:363-377 is not listed on IDEAS

    More about this item


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cup:etheor:v:24:y:2008:i:03:p:749-794_08. 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: (Keith Waters). General contact details of provider: .

    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.

    We have no references for this item. You can help adding them by using 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 RePEc Author Service 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.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.