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A fast score test for generalized mixture models

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Listed:
  • Rui Duan
  • Yang Ning
  • Shuang Wang
  • Bruce G. Lindsay
  • Raymond J. Carroll
  • Yong Chen

Abstract

In biomedical studies, testing for homogeneity between two groups, where one group is modeled by mixture models, is often of great interest. This paper considers the semiparametric exponential family mixture model proposed by Hong et al. (2017) and studies the score test for homogeneity under this model. The score test is nonregular in the sense that nuisance parameters disappear under the null hypothesis. To address this difficulty, we propose a modification of the score test, so that the resulting test enjoys the Wilks phenomenon. In finite samples, we show that with fixed nuisance parameters the score test is locally most powerful. In large samples, we establish the asymptotic power functions under two types of local alternative hypotheses. Our simulation studies illustrate that the proposed score test is powerful and computationally fast. We apply the proposed score test to an UK ovarian cancer DNA methylation data for identification of differentially methylated CpG sites.

Suggested Citation

  • Rui Duan & Yang Ning & Shuang Wang & Bruce G. Lindsay & Raymond J. Carroll & Yong Chen, 2020. "A fast score test for generalized mixture models," Biometrics, The International Biometric Society, vol. 76(3), pages 811-820, September.
    • Handle: RePEc:bla:biomet:v:76:y:2020:i:3:p:811-820
    DOI: 10.1111/biom.13204
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    References listed on IDEAS

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    1. Chong-Zhi Di & Kung-Yee Liang, 2011. "Likelihood Ratio Testing for Admixture Models with Application to Genetic Linkage Analysis," Biometrics, The International Biometric Society, vol. 67(4), pages 1249-1259, December.
    2. Wessel N. van Wieringen & Mark A. van de Wiel, 2009. "Nonparametric Testing for DNA Copy Number Induced Differential mRNA Gene Expression," Biometrics, The International Biometric Society, vol. 65(1), pages 19-29, March.
    3. Hanfeng Chen & Jiahua Chen & John D. Kalbfleisch, 2001. "A modified likelihood ratio test for homogeneity in finite mixture models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(1), pages 19-29.
    4. 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.
    5. Yang Ning & Yong Chen, 2015. "A Class of Pseudolikelihood Ratio Tests for Homogeneity in Exponential Tilt Mixture Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(2), pages 504-517, June.
    6. Kung-Yee Liang & Paul J. Rathouz, 1999. "Hypothesis Testing Under Mixture Models: Application to Genetic Linkage Analysis," Biometrics, The International Biometric Society, vol. 55(1), pages 65-74, March.
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    Cited by:

    1. Yinan Li & Kai-Tai Fang & Ping He & Heng Peng, 2022. "Representative Points from a Mixture of Two Normal Distributions," Mathematics, MDPI, vol. 10(21), pages 1-28, October.

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