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

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  • Bierens, Herman J.

Abstract

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(3), pages 749-794, June.
    • Handle: RePEc:cup:etheor:v:24:y:2008:i:03:p:749-794_08
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    Citations

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    Cited by:

    1. Yang Lu, 2019. "Flexible (panel) regression models for bivariate count–continuous data with an insurance application," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 182(4), pages 1503-1521, October.
    2. Arulampalam, Wiji & Corradi, Valentina & Gutknecht, Daniel, 2017. "Modeling heaped duration data: An application to neonatal mortality," Journal of Econometrics, Elsevier, vol. 200(2), pages 363-377.
    3. JoonHwan Cho & Yao Luo & Ruli Xiao, 2022. "Deconvolution from Two Order Statistics," Working Papers tecipa-739, University of Toronto, Department of Economics.
    4. Lu, Zhentong & Shi, Xiaoxia & Tao, Jing, 2023. "Semi-nonparametric estimation of random coefficients logit model for aggregate demand," Journal of Econometrics, Elsevier, vol. 235(2), pages 2245-2265.
    5. Bierens Herman J & Carvalho Jose R, 2011. "Job Search, Conditional Treatment and Recidivism: The Employment Services for Ex-Offenders Program Reconsidered," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 11(1), pages 1-40, January.
    6. Sukjin Han & Sungwon Lee, 2019. "Estimation in a generalization of bivariate probit models with dummy endogenous regressors," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(6), pages 994-1015, September.
    7. Haiqing Xu, 2010. "Social Interactions: A Game Theoretic Approach," Department of Economics Working Papers 130914, The University of Texas at Austin, Department of Economics.
    8. 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.
    9. 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.
    10. Ye, Xin & Garikapati, Venu M. & You, Daehyun & Pendyala, Ram M., 2017. "A practical method to test the validity of the standard Gumbel distribution in logit-based multinomial choice models of travel behavior," Transportation Research Part B: Methodological, Elsevier, vol. 106(C), pages 173-192.
    11. 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.
    12. Fosgerau, Mogens & Mabit, Stefan L., 2013. "Easy and flexible mixture distributions," Economics Letters, Elsevier, vol. 120(2), pages 206-210.
    13. Mogens Fosgerau, 2024. "Nonparametric approaches to describing heterogeneity," Chapters, in: Stephane Hess & Andrew Daly (ed.), Handbook of Choice Modelling, chapter 11, pages 308-318, Edward Elgar Publishing.
    14. Christian N. Brinch, 2008. "Non-parametric Identification of the Mixed Hazards Model with Interval-Censored Durations," Discussion Papers 539, Statistics Norway, Research Department.
    15. Fosgerau, Mogens & Hess, Stephane, 2008. "Competing methods for representing random taste heterogeneity in discrete choice models," MPRA Paper 10038, University Library of Munich, Germany.
    16. 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.

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