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Likelihood inference in some finite mixture models

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  • Chen, Xiaohong
  • Ponomareva, Maria
  • Tamer, Elie

Abstract

Parametric mixture models are commonly used in applied work, especially empirical economics, where these models are often employed to learn for example about the proportions of various types in a given population. This paper examines the inference question on the proportions (mixing probability) in a simple mixture model in the presence of nuisance parameters when sample size is large. It is well known that likelihood inference in mixture models is complicated due to (1) lack of point identification, and (2) parameters (for example, mixing probabilities) whose true value may lie on the boundary of the parameter space. These issues cause the profiled likelihood ratio (PLR) statistic to admit asymptotic limits that differ discontinuously depending on how the true density of the data approaches the regions of singularities where there is lack of point identification. This lack of uniformity in the asymptotic distribution suggests that confidence intervals based on pointwise asymptotic approximations might lead to faulty inferences. This paper examines this problem in details in a finite mixture model and provides possible fixes based on the parametric bootstrap. We examine the performance of this parametric bootstrap in Monte Carlo experiments and apply it to data from Beauty Contest experiments. We also examine small sample inferences and projection methods.

Suggested Citation

  • Chen, Xiaohong & Ponomareva, Maria & Tamer, Elie, 2014. "Likelihood inference in some finite mixture models," Journal of Econometrics, Elsevier, vol. 182(1), pages 87-99.
  • Handle: RePEc:eee:econom:v:182:y:2014:i:1:p:87-99
    DOI: 10.1016/j.jeconom.2014.04.010
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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.
    2. Xu Cheng, 2014. "Uniform Inference in Nonlinear Models with Mixed Identification Strength," PIER Working Paper Archive 14-018, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    3. Jiaying Gu & Roger Koenker & Stanislav Volgushev, 2017. "Testing for homogeneity in mixture models," CeMMAP working papers CWP39/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. Donald W. K. Andrews & Patrik Guggenberger, 2015. "Identification- and Singularity-Robust Inference for Moment Condition," Cowles Foundation Discussion Papers 1978R, Cowles Foundation for Research in Economics, Yale University, revised Oct 2018.
    5. Chen, Heng & Fan, Yanqin & Liu, Ruixuan, 2016. "Inference for the correlation coefficient between potential outcomes in the Gaussian switching regime model," Journal of Econometrics, Elsevier, vol. 195(2), pages 255-270.
    6. Cheng, Xu, 2015. "Robust inference in nonlinear models with mixed identification strength," Journal of Econometrics, Elsevier, vol. 189(1), pages 207-228.

    More about this item

    Keywords

    Finite mixtures; Parametric bootstrap; Profiled likelihood ratio statistic;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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