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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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    Cited by:

    1. Yiping Yang & Peixin Zhao & Dongsheng Wu, 2025. "Robust variable selection with exponential squared loss for linear mixed-effects models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 88(6), pages 1023-1049, August.
    2. 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.
    3. 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.
    4. 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.
    5. Yiping Yang & Peixin Zhao & Dongsheng Wu, 2025. "Robust variable selection with exponential squared loss for linear mixed-effects models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 88(7), pages 981-1007, October.
    6. 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.
    7. 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.
    8. 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.
    9. Yang, Yiping & Luo, Chuanqin & Yang, Weiming, 2024. "Double penalized variable selection for high-dimensional partial linear mixed effects models," Journal of Multivariate Analysis, Elsevier, vol. 204(C).
    10. 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.
    11. Dan Ben-Moshe & David Genesove, 2026. "Unbiased Estimation of Central Moments in Unbalanced Two- and Three-Level Models," Papers 2602.03469, arXiv.org, revised Mar 2026.
    12. 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.
    13. 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.

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