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Likelihood Inference in Some Finite Mixture Models

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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.

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  • Xiaohong Chen & Maria Ponomareva & Elie Tamer, 2013. "Likelihood Inference in Some Finite Mixture Models," Cowles Foundation Discussion Papers 1895, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1895
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    1. Stahl Dale O. & Wilson Paul W., 1995. "On Players' Models of Other Players: Theory and Experimental Evidence," Games and Economic Behavior, Elsevier, vol. 10(1), pages 218-254, July.
    2. Antoni Bosch-Domènech & José G. Montalvo & Rosemarie Nagel & Albert Satorra, 2002. "One, Two, (Three), Infinity, ...: Newspaper and Lab Beauty-Contest Experiments," American Economic Review, American Economic Association, vol. 92(5), pages 1687-1701, December.
    3. Dufour, Jean-Marie, 2006. "Monte Carlo tests with nuisance parameters: A general approach to finite-sample inference and nonstandard asymptotics," Journal of Econometrics, Elsevier, vol. 133(2), pages 443-477, August.
    4. Andrews, Donald W.K. & Cheng, Xu, 2013. "Maximum likelihood estimation and uniform inference with sporadic identification failure," Journal of Econometrics, Elsevier, vol. 173(1), pages 36-56.
    5. Andrews, Donald W.K. & Cheng, Xu & Guggenberger, Patrik, 2020. "Generic results for establishing the asymptotic size of confidence sets and tests," Journal of Econometrics, Elsevier, vol. 218(2), pages 496-531.
    6. Antoni Bosch-Domènech & José Montalvo & Rosemarie Nagel & Albert Satorra, 2010. "A finite mixture analysis of beauty-contest data using generalized beta distributions," Experimental Economics, Springer;Economic Science Association, vol. 13(4), pages 461-475, December.
    7. Keane, Michael P & Wolpin, Kenneth I, 1997. "The Career Decisions of Young Men," Journal of Political Economy, University of Chicago Press, vol. 105(3), pages 473-522, June.
    8. Donald W. K. Andrews & Xu Cheng, 2012. "Estimation and Inference With Weak, Semi‐Strong, and Strong Identification," Econometrica, Econometric Society, vol. 80(5), pages 2153-2211, September.
    9. Costa-Gomes, Miguel & Crawford, Vincent P & Broseta, Bruno, 2001. "Cognition and Behavior in Normal-Form Games: An Experimental Study," Econometrica, Econometric Society, vol. 69(5), pages 1193-1235, September.
    10. Victor Chernozhukov & Han Hong & Elie Tamer, 2007. "Estimation and Confidence Regions for Parameter Sets in Econometric Models," Econometrica, Econometric Society, vol. 75(5), pages 1243-1284, September.
    11. Jin Seo Cho & Halbert White, 2007. "Testing for Regime Switching," Econometrica, Econometric Society, vol. 75(6), pages 1671-1720, November.
    12. Hanfeng Chen & Jiahua Chen & John D. Kalbfleisch, 2004. "Testing for a finite mixture model with two components," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 95-115, February.
    13. Anna Mikusheva, 2007. "Uniform Inference in Autoregressive Models," Econometrica, Econometric Society, vol. 75(5), pages 1411-1452, September.
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    Cited by:

    1. Yan, Cheng & Cheng, Tingting, 2019. "In search of the optimal number of fund subgroups," Journal of Empirical Finance, Elsevier, vol. 50(C), pages 78-92.
    2. Hiroyuki Kasahara & Katsumi Shimotsu, 2018. "Testing the Number of Regimes in Markov Regime Switching Models," Papers 1801.06862, arXiv.org, revised Jan 2018.
    3. 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.
    4. Jiaying Gu & Roger Koenker & Stanislav Volgushev, 2017. "Testing for homogeneity in mixture models," CeMMAP working papers 39/17, Institute for Fiscal Studies.
    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. Donald W. K. Andrews & Patrik Guggenberger, 2015. "Identification- and Singularity-Robust Inference for Moment Condition," Cowles Foundation Discussion Papers 1978, Cowles Foundation for Research in Economics, Yale University.
    7. 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.
    8. Cheng, Xu, 2015. "Robust inference in nonlinear models with mixed identification strength," Journal of Econometrics, Elsevier, vol. 189(1), pages 207-228.
    9. Yu Hao & Hiroyuki Kasahara, 2022. "Testing the Number of Components in Finite Mixture Normal Regression Model with Panel Data," Papers 2210.02824, arXiv.org, revised Jun 2023.
    10. 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.
    11. Jean-Jacques Forneron, 2019. "A Sieve-SMM Estimator for Dynamic Models," Papers 1902.01456, arXiv.org, revised Jan 2023.
    12. David Pacini, 2022. "A Goodness-of-Identifiability Criterion for Parametric Statistical Models," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 11(4), pages 1-1.

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    More about this item

    Keywords

    Finite mixtures; Parametric bootstrap; Profiled likelihood ratio statistic; Partial identification; Parameter on the boundary;
    All these keywords.

    JEL classification:

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

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