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Non-finite Fisher information and homogeneity: an EM approach

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  • P. Li
  • J. Chen
  • P. Marriott

Abstract

Even simple examples of finite mixture models can fail to fulfil the regularity conditions that are routinely assumed in standard parametric inference problems. Many methods have been investigated for testing for homogeneity in finite mixture models, for example, but all rely on regularity conditions including the finiteness of the Fisher information and the space of the mixing parameter being a compact subset of some Euclidean space. Very simple examples where such assumptions fail include mixtures of two geometric distributions and two exponential distributions, and, more generally, mixture models in scale distribution families. To overcome these difficulties, we propose and study an em -test statistic, which has a simple limiting distribution for examples in this paper. Simulations show that the em -test has accurate Type I errors and is more efficient than existing methods when they are applicable. A real example is included. Copyright 2009, Oxford University Press.

Suggested Citation

  • P. Li & J. Chen & P. Marriott, 2009. "Non-finite Fisher information and homogeneity: an EM approach," Biometrika, Biometrika Trust, vol. 96(2), pages 411-426.
    • Handle: RePEc:oup:biomet:v:96:y:2009:i:2:p:411-426
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    Cited by:

    1. Yang Liu & Rong Kuang & Guanfu Liu, 2024. "Penalized likelihood inference for the finite mixture of Poisson distributions from capture-recapture data," Statistical Papers, Springer, vol. 65(5), pages 2751-2773, July.
    2. Hiroyuki Kasahara & Katsumi Shimotsu, 2012. "Testing the Number of Components in Finite Mixture Models," CIRJE F-Series CIRJE-F-867, CIRJE, Faculty of Economics, University of Tokyo.
    3. David Pacini, 2022. "Identification in Parametric Models: The Minimum Hellinger Distance Criterion," Econometrics, MDPI, vol. 10(1), pages 1-14, February.
    4. Jiaying Gu & Roger Koenker & Stanislav Volgushev, 2017. "Testing for homogeneity in mixture models," CeMMAP working papers 39/17, Institute for Fiscal Studies.
    5. Charnigo, Richard & Fan, Qian & Bittel, Douglas & Dai, Hongying, 2013. "Testing unilateral versus bilateral normal contamination," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 163-167.
    6. Ker, Alan. P & Tolhurst, Tor & Liu, Yong, 2015. "Rating Area-yield Crop Insurance Contracts Using Bayesian Model Averaging and Mixture Models," 2015 AAEA & WAEA Joint Annual Meeting, July 26-28, San Francisco, California 205211, Agricultural and Applied Economics Association.
    7. Shaoting Li & Jiahua Chen, 2023. "Mixture of shifted binomial distributions for rating data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(5), pages 833-853, October.
    8. 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.
    9. Chuan Hong & Yang Ning & Shuang Wang & Hao Wu & Raymond J. Carroll & Yong Chen, 2017. "PLEMT: A Novel Pseudolikelihood-Based EM Test for Homogeneity in Generalized Exponential Tilt Mixture Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1393-1404, October.
    10. Variyath A. M. & Vasudevan C. V., 2013. "An Application of EM Test for the Bayesian Change Point Problem," Stochastics and Quality Control, De Gruyter, vol. 28(1), pages 57-69, October.
    11. Wong, Tony S.T. & Lam, Kwok Fai & Zhao, Victoria X., 2018. "Asymptotic null distribution of the modified likelihood ratio test for homogeneity in finite mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 248-257.
    12. Wong, Tony Siu Tung & Li, Wai Keung, 2014. "Test for homogeneity in gamma mixture models using likelihood ratio," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 127-137.
    13. Hiroyuki Kasahara & Katsumi Shimotsu, 2017. "Testing the Order of Multivariate Normal Mixture Models," CIRJE F-Series CIRJE-F-1044, CIRJE, Faculty of Economics, University of Tokyo.
    14. Christian Ritz, 2013. "Penalized likelihood ratio tests for repeated measurement models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 534-547, September.
    15. Bagkavos, Dimitrios & Patil, Prakash N., 2023. "Goodness-of-fit testing for normal mixture densities," Computational Statistics & Data Analysis, Elsevier, vol. 188(C).

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