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Inference on Mixtures Under Tail Restrictions

Author

Listed:
  • Marc Henry

    (Départment de sciences économiques)

  • Koen Jochmans

    (Département d'économie (ECON))

  • Bernard Salanié

    (Department of Economics (Columbia))

Abstract

Many econometric models can be analyzed as finite mixtures. We focus on two-component mixtures and we show that they are nonparametrically point identified by a combination of an exclusion restriction and tail restrictions. Our identification analysis suggests simple closed-form estimators of the component distributions and mixing proportions. We derive their asymptotic properties using results on tail empirical processes and we present a simulation study that documents their finite-sample performance.

Suggested Citation

  • Marc Henry & Koen Jochmans & Bernard Salanié, 2015. "Inference on Mixtures Under Tail Restrictions," Sciences Po publications 2014-01, Sciences Po.
    • Handle: RePEc:spo:wpmain:info:hdl:2441/f6h8764enu2lskk9p2m96cphi
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    References listed on IDEAS

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    1. Arthur Lewbel, 2007. "Estimation of Average Treatment Effects with Misclassification," Econometrica, Econometric Society, vol. 75(2), pages 537-551, March.
    2. V. Chernozhukov & I. Fernández-Val & A. Galichon, 2009. "Improving point and interval estimators of monotone functions by rearrangement," Biometrika, Biometrika Trust, vol. 96(3), pages 559-575.
    3. Donald W. K. Andrews & Marcia M. A. Schafgans, 1998. "Semiparametric Estimation of the Intercept of a Sample Selection Model," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 497-517.
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    5. Stéphane Bonhomme & Koen Jochmans & Jean-Marc Robin, 2013. "Nonparametric estimation of finite mixtures," SciencePo Working papers hal-00972868, HAL.
    6. Aprajit Mahajan, 2006. "Identification and Estimation of Regression Models with Misclassification," Econometrica, Econometric Society, vol. 74(3), pages 631-665, May.
    7. Laurent Bordes & Céline Delmas & Pierre Vandekerkhove, 2006. "Semiparametric Estimation of a Two‐component Mixture Model where One Component is known," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(4), pages 733-752, December.
    8. Bollinger, Christopher R., 1996. "Bounding mean regressions when a binary regressor is mismeasured," Journal of Econometrics, Elsevier, vol. 73(2), pages 387-399, August.
    9. repec:hal:spmain:info:hdl:2441/7o52iohb7k6srk09n8t4k21sm is not listed on IDEAS
    10. V. Chernozhukov & I. Fernández-Val & A. Galichon, 2009. "Improving point and interval estimators of monotone functions by rearrangement," Biometrika, Biometrika Trust, vol. 96(3), pages 559-575.
    11. Hiroyuki Kasahara & Katsumi Shimotsu, 2009. "Nonparametric Identification of Finite Mixture Models of Dynamic Discrete Choices," Econometrica, Econometric Society, vol. 77(1), pages 135-175, January.
    12. repec:hal:wpspec:info:hdl:2441/7o52iohb7k6srk09n8t4k21sm is not listed on IDEAS
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    Citations

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    Cited by:

    1. Jochmans, Koen & Henry, Marc & Salanié, Bernard, 2017. "Inference On Two-Component Mixtures Under Tail Restrictions," Econometric Theory, Cambridge University Press, vol. 33(3), pages 610-635, June.
    2. Stéphane Bonhomme & Koen Jochmans & Jean-Marc Robin, 2014. "Estimating Multivariate Latent-Structure Models," SciencePo Working papers Main hal-01097135, HAL.
    3. Stéphane Bonhomme & Koen Jochmans & Jean-Marc Robin, 2014. "Nonparametric spectral-based estimation of latent structures," CeMMAP working papers 18/14, Institute for Fiscal Studies.
    4. Jean-Marc Robin & Stéphane Bonhomme & Koen Jochmans, 2014. "Estimating Multivariate Latent-Structure Models," Sciences Po Economics Discussion Papers 2014-18, Sciences Po Departement of Economics.
    5. repec:hal:wpspec:info:hdl:2441/2i27dd3b6h94aarftq0slq652a is not listed on IDEAS
    6. repec:hal:spmain:info:hdl:2441/2i27dd3b6h94aarftq0slq652a is not listed on IDEAS
    7. repec:hal:spmain:info:hdl:2441/etefo8s8r89oamhnhiclqr530 is not listed on IDEAS

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    Keywords

    mixture model; nonparametric identification and estimation; tail empirical process;
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