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An Orthogonality‐Based Estimation of Moments for Linear Mixed Models

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  • PING WU
  • LI XING ZHU

Abstract

. Estimating higher‐order moments, particularly fourth‐order moments in linear mixed models is an important, but difficult issue. In this article, an orthogonality‐based estimation of moments is proposed. Under only moment conditions, this method can easily be used to estimate the model parameters and moments, particularly those of higher order than the second order, and in the estimators the random effects and errors do not affect each other. The asymptotic normality of all the estimators is provided. Moreover, the method is readily extended to handle non‐linear, semiparametric and non‐linear models. A simulation study is carried out to examine the performance of the new method.

Suggested Citation

  • Ping Wu & Li Xing Zhu, 2010. "An Orthogonality‐Based Estimation of Moments for Linear Mixed Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(2), pages 253-263, June.
    • Handle: RePEc:bla:scjsta:v:37:y:2010:i:2:p:253-263
    DOI: 10.1111/j.1467-9469.2009.00673.x
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    References listed on IDEAS

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    1. Rao, C. Radhakrishna, 1971. "Estimation of variance and covariance components--MINQUE theory," Journal of Multivariate Analysis, Elsevier, vol. 1(3), pages 257-275, September.
    2. D. R. Cox, 2002. "Estimation in a simple random effects model with nonnormal distributions," Biometrika, Biometrika Trust, vol. 89(4), pages 831-840, December.
    3. Heyde, C. C., 1994. "A quasi-likelihood approach to the REML estimating equations," Statistics & Probability Letters, Elsevier, vol. 21(5), pages 381-384, December.
    4. Cui, Hengjian & Ng, Kai W. & Zhu, Lixing, 2004. "Estimation in mixed effects model with errors in variables," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 53-73, October.
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    Cited by:

    1. Gwennaëlle Mabon, 2014. "Adaptive Estimation of Random-Effects Densities In Linear Mixed-Effects Model," Working Papers 2014-41, Center for Research in Economics and Statistics.
    2. Soberón, Alexandra & Stute, Winfried, 2017. "Assessing skewness, kurtosis and normality in linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 161(C), pages 123-140.
    3. Ping Wu & Xinchao Luo & Peirong Xu & Lixing Zhu, 2017. "New variable selection for linear mixed-effects models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(3), pages 627-646, June.
    4. Wu, Jianhong & Qin, Jinxu & Ding, Qing, 2015. "A moment-based test for individual effects in the error component model with incomplete panels," Statistics & Probability Letters, Elsevier, vol. 104(C), pages 153-162.
    5. Jianhong Wu & Lixing Zhu, 2012. "Estimation of and testing for random effects in dynamic panel data models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 477-497, September.
    6. Wu, Jianhong & Li, Guodong, 2014. "Moment-based tests for individual and time effects in panel data models," Journal of Econometrics, Elsevier, vol. 178(P3), pages 569-581.
    7. Zhao, Yan-Yong & Lin, Jin-Guan & Xu, Pei-Rong & Ye, Xu-Guo, 2015. "Orthogonality-projection-based estimation for semi-varying coefficient models with heteroscedastic errors," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 204-221.
    8. Mariano Ruiz Espejo & Miguel Delgado Pineda & Saralees Nadarajah, 2013. "Optimal unbiased estimation of some population central moments," METRON, Springer;Sapienza Università di Roma, vol. 71(1), pages 39-62, June.
    9. Fabienne Comte & Adeline Samson, 2012. "Nonparametric estimation of random-effects densities in linear mixed-effects model," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(4), pages 951-975, December.

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