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Tests in variance components models under skew-normal settings

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  • Rendao Ye
  • Tonghui Wang
  • Saowanit Sukparungsee
  • Arjun Gupta

Abstract

The hypothesis testing problems of unknown parameters for the variance components model with skew-normal random errors are discussed. Several properties of the model, such as the density function, moment generating function, and independence conditions, are obtained. A new version of Cochran’s theorem is given, which is used to establish exact tests for fixed effects and variance components of the model. For illustration, our main results are applied to two examples and a real data problem. Finally, some simulation results on the type I error probability and power of the proposed test are reported. And the simulation results indicate that the proposed test provides satisfactory performance on the type I error probability and power. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Rendao Ye & Tonghui Wang & Saowanit Sukparungsee & Arjun Gupta, 2015. "Tests in variance components models under skew-normal settings," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(7), pages 885-904, October.
    • Handle: RePEc:spr:metrik:v:78:y:2015:i:7:p:885-904
    DOI: 10.1007/s00184-015-0532-1
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    References listed on IDEAS

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    1. Huageng Tao & Mari Palta & Brian S. Yandell & Michael A. Newton, 1999. "An Estimation Method for the Semiparametric Mixed Effects Model," Biometrics, The International Biometric Society, vol. 55(1), pages 102-110, March.
    2. Mi-Xia Wu & Kai-Fun Yu & Aiyi Liu & Tie-Feng Ma, 2012. "Simultaneous optimal estimation in linear mixed models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(4), pages 471-489, May.
    3. Verbeke, Geert & Lesaffre, Emmanuel, 1997. "The effect of misspecifying the random-effects distribution in linear mixed models for longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 23(4), pages 541-556, February.
    4. ., 1999. "The assessment of capital adequacy," Chapters, in: Handbook of Banking Regulation and Supervision in the United Kingdom, chapter 17, Edward Elgar Publishing.
    5. Wang, Tonghui & Li, Baokun & Gupta, Arjun K., 2009. "Distribution of quadratic forms under skew normal settings," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 533-545, March.
    6. Lounasheimo, Antton, 1999. "The Impact of Human Capital on Economic Growth," Discussion Papers 673, The Research Institute of the Finnish Economy.
    7. Daowen Zhang & Marie Davidian, 2001. "Linear Mixed Models with Flexible Distributions of Random Effects for Longitudinal Data," Biometrics, The International Biometric Society, vol. 57(3), pages 795-802, September.
    8. Ye, Rendao & Wang, Tonghui & Gupta, Arjun K., 2014. "Distribution of matrix quadratic forms under skew-normal settings," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 229-239.
    9. Wendimagegn Ghidey & Emmanuel Lesaffre & Paul Eilers, 2004. "Smooth Random Effects Distribution in a Linear Mixed Model," Biometrics, The International Biometric Society, vol. 60(4), pages 945-953, December.
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