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Testing for homogeneity in mixture models

Author

Listed:
  • Jiaying Gu

    () (Institute for Fiscal Studies and University of Toronto)

  • Roger Koenker

    () (Institute for Fiscal Studies and University of Illinois)

  • Stanislav Volgushev

    (Institute for Fiscal Studies)

Abstract

Statistical models of unobserved heterogeneity are typically formalised as mixtures of simple parametric models and interest naturally focuses on testing for homogeneity versus general mixture alternatives. Many tests of this type can be interpreted as C(a) tests, as in Neyman (1959), and shown to be locally, asymptotically optimal. A unified approach to analysing the asymptotic behaviour of such tests will be described, employing a variant of the LeCam LAN framework. These C(a) tests will be contrasted with a new approach to likelihood ratio testing for mixture models. The latter tests are based on estimation of general (nonparametric) mixture models using the Kiefer and Wolfowitz (1956) maximum likelihood method. Recent developments in convex optimisation are shown to dramatically improve upon earlier EM methods for computation of these estimators, and new results on the large sample behaviour of likelihood rations involving such estimators yield a tractable form of asymptotic inference. We compare performance of the two approaches identifying circumstances in which each is preferred.

Suggested Citation

  • Jiaying Gu & Roger Koenker & Stanislav Volgushev, 2013. "Testing for homogeneity in mixture models," CeMMAP working papers CWP09/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:09/13
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    File URL: http://www.cemmap.ac.uk/wps/cwp091313.pdf
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    References listed on IDEAS

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    1. Yingying Dong & Arthur Lewbel & Thomas Tao Yang, 2012. "Comparing Features of Convenient Estimators for Binary Choice Models With Endogenous Regressors," Boston College Working Papers in Economics 789, Boston College Department of Economics, revised 15 May 2012.
    2. Victor Chernozhukov & Sokbae Lee & Adam M. Rosen, 2013. "Intersection Bounds: Estimation and Inference," Econometrica, Econometric Society, vol. 81(2), pages 667-737, March.
    3. Azeem M. Shaikh & Edward J. Vytlacil, 2011. "Partial Identification in Triangular Systems of Equations With Binary Dependent Variables," Econometrica, Econometric Society, vol. 79(3), pages 949-955, May.
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    Cited by:

    1. Sergei Koulayev & Marc Rysman & Scott Schuh & Joanna Stavins, 2016. "Explaining adoption and use of payment instruments by US consumers," RAND Journal of Economics, RAND Corporation, vol. 47(2), pages 293-325, May.

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