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Semiparametric mixture: Continuous scale mixture approach

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  • Xiang, Sijia
  • Yao, Weixin
  • Seo, Byungtae

Abstract

In this article, we propose a new estimation procedure for a class of semiparametric mixture models that is a mixture of unknown location-shifted symmetric distributions. The proposed method assumes that the nonparametric symmetric distribution falls in a rich class of continuous normal scale mixture distributions. With this new modeling approach, we can suitably avoid the misspecification problem in traditional parametric mixture models. In addition, unlike some existing semiparametric methods, the proposed method does not require any modification or smoothing of the likelihood as it can directly estimate parametric and nonparametric components simultaneously in the model. Furthermore, the proposed parameter estimates are robust against outliers. The estimation algorithms are introduced and numerical studies are conducted to examine the finite sample performance of the proposed procedure and to compare it with other existing methods.

Suggested Citation

  • Xiang, Sijia & Yao, Weixin & Seo, Byungtae, 2016. "Semiparametric mixture: Continuous scale mixture approach," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 413-425.
    • Handle: RePEc:eee:csdana:v:103:y:2016:i:c:p:413-425
    DOI: 10.1016/j.csda.2016.06.001
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    References listed on IDEAS

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    1. Matthew Stephens, 2000. "Dealing with label switching in mixture models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 795-809.
    2. 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.
    3. Yong Wang, 2007. "On fast computation of the non‐parametric maximum likelihood estimate of a mixing distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(2), pages 185-198, April.
    4. Basu, Sanjib, 1996. "Existence of a normal scale mixture with a given variance and a percentile," Statistics & Probability Letters, Elsevier, vol. 28(2), pages 115-120, June.
    5. Yao, Weixin & Lindsay, Bruce G., 2009. "Bayesian Mixture Labeling by Highest Posterior Density," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 758-767.
    6. Laurent Bordes & Céline Delmas & Pierre Vandekerkhove, 2006. "Semiparametric Estimation of a Two‐component Mixture Model where One Component is known," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(4), pages 733-752, December.
    7. Seo, Byungtae & Kim, Daeyoung, 2012. "Root selection in normal mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 56(8), pages 2454-2470.
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    Cited by:

    1. Byungtae Seo & Sangwook Kang, 2023. "Accelerated failure time modeling via nonparametric mixtures," Biometrics, The International Biometric Society, vol. 79(1), pages 165-177, March.
    2. Yanyuan Ma & Shaoli Wang & Lin Xu & Weixin Yao, 2021. "Semiparametric mixture regression with unspecified error distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(2), pages 429-444, June.

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