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Almost nonparametric inference for repeated measures in mixture models

Author

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  • T. P. Hettmansperger
  • Hoben Thomas

Abstract

We consider ways to estimate the mixing proportions in a finite mixture distribution or to estimate the number of components of the mixture distribution without making parametric assumptions about the component distributions. We require a vector of observations on each subject. This vector is mapped into a vector of 0s and 1s and summed. The resulting distribution of sums can be modelled as a mixture of binomials. We then work with the binomial mixture. The efficiency and robustness of this method are compared with the strategy of assuming multivariate normal mixtures when, typically, the true underlying mixture distribution is different. It is shown that in many cases the approach based on simple binomial mixtures is superior.

Suggested Citation

  • T. P. Hettmansperger & Hoben Thomas, 2000. "Almost nonparametric inference for repeated measures in mixture models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 811-825.
    • Handle: RePEc:bla:jorssb:v:62:y:2000:i:4:p:811-825
    DOI: 10.1111/1467-9868.00266
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    Cited by:

    1. Stéphane Bonhomme & Koen Jochmans & Jean-Marc Robin, 2014. "Nonparametric spectral-based estimation of latent structures," CeMMAP working papers CWP18/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Hiroyuki Kasahara & Katsumi Shimotsu, 2014. "Non-parametric identification and estimation of the number of components in multivariate mixtures," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(1), pages 97-111, January.
    3. Arabind Yadav, 2016. "Long-term earthquake forecasting model for northeast India and surrounding region: seismicity-based model," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 80(1), pages 173-190, January.
    4. repec:spo:wpmain:info:hdl:2441/etefo8s8r89oamhnhiclqr530 is not listed on IDEAS
    5. Davide Di Cecco, 2012. "Conditional exact tests for Markovianity and reversibility in multiple categorical sequences," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(1), pages 170-187, March.
    6. Loperfido, Nicola, 2013. "Skewness and the linear discriminant function," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 93-99.
    7. Stéphane Bonhomme & Koen Jochmans & Jean-Marc Robin, 2016. "Non-parametric estimation of finite mixtures from repeated measurements," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(1), pages 211-229, January.
    8. Kasahara, Hiroyuki & Shimotsu, Katsumi, 2007. "Nonparametric Identification and Estimation of Multivariate Mixtures," Queen's Economics Department Working Papers 273629, Queen's University - Department of Economics.
    9. Nicolas Picard & Avner Bar-Hen, 2012. "A Criterion Based on the Mahalanobis Distance for Cluster Analysis with Subsampling," Journal of Classification, Springer;The Classification Society, vol. 29(1), pages 23-49, April.
    10. Hema Yoganarasimhan, 2016. "Estimation of Beauty Contest Auctions," Marketing Science, INFORMS, vol. 35(1), pages 27-54, January.
    11. Stéphane Bonhomme & Koen Jochmans & Jean-Marc Robin, 2014. "Estimating Multivariate Latent-Structure Models," Sciences Po Economics Publications (main) hal-01097135, HAL.
    12. Christian Tien, 2022. "Instrumented Common Confounding," Papers 2206.12919, arXiv.org, revised Sep 2022.
    13. Bordes, Laurent & Chauveau, Didier & Vandekerkhove, Pierre, 2007. "A stochastic EM algorithm for a semiparametric mixture model," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5429-5443, July.
    14. 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.

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