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A Class of Pseudolikelihood Ratio Tests for Homogeneity in Exponential Tilt Mixture Models

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  • Yang Ning
  • Yong Chen

Abstract

type="main" xml:id="sjos12119-abs-0001"> Mixture models are commonly used in biomedical research to account for possible heterogeneity in population. In this paper, we consider tests for homogeneity between two groups in the exponential tilt mixture models. A novel pairwise pseudolikelihood approach is proposed to eliminate the unknown nuisance function. We show that the corresponding pseudolikelihood ratio test has an asymptotic distribution as a supremum of two squared Gaussian processes under the null hypothesis. To maintain the appeal of simplicity for conventional likelihood ratio tests, we propose two alternative tests, both shown to have a simple asymptotic distribution of χ 1 2 under the null. Simulation studies show that the proposed class of pseudolikelihood ratio tests performs well in controlling type I errors and having competitive powers compared with the current tests. The proposed tests are illustrated by an example of partial differential expression detection using microarray data from prostate cancer patients.

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  • 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.
    • Handle: RePEc:bla:scjsta:v:42:y:2015:i:2:p:504-517
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    File URL: http://hdl.handle.net/10.1111/sjos.12119
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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. 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.
    3. 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.
    4. Lemdani, Mohamed & Pons, Odile, 1997. "Likelihood ratio tests for genetic linkage," Statistics & Probability Letters, Elsevier, vol. 33(1), pages 15-22, April.
    5. 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.
    6. Hong‐Tu Zhu & Heping Zhang, 2004. "Hypothesis testing in mixture regression models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 3-16, February.
    7. Jing Qin & Kung-Yee Liang, 2011. "Hypothesis Testing in a Mixture Case–Control Model," Biometrics, The International Biometric Society, vol. 67(1), pages 182-193, March.
    8. F. Zou, 2002. "On empirical likelihood for a semiparametric mixture model," Biometrika, Biometrika Trust, vol. 89(1), pages 61-75, March.
    9. Lancaster, Tony & Imbens, Guido, 1996. "Case-control studies with contaminated controls," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 145-160.
    10. van Wieringen, Wessel N & van de Wiel, Mark A & van der Vaart, Aad W, 2008. "A Test for Partial Differential Expression," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 1039-1049.
    11. Yong Chen & Kung-Yee Liang, 2010. "On the asymptotic behaviour of the pseudolikelihood ratio test statistic with boundary problems," Biometrika, Biometrika Trust, vol. 97(3), pages 603-620.
    12. Z. Tan, 2009. "A note on profile likelihood for exponential tilt mixture models," Biometrika, Biometrika Trust, vol. 96(1), pages 229-236.
    13. 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.
    14. D. R. Cox, 2004. "A note on pseudolikelihood constructed from marginal densities," Biometrika, Biometrika Trust, vol. 91(3), pages 729-737, September.
    15. Kung‐Yee Liang & Jing Qin, 2000. "Regression analysis under non‐standard situations: a pairwise pseudolikelihood approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 773-786.
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