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Efficient robust estimation for single-index mixed effects models with missing observations

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  • Liugen Xue

    (Henan University)

  • Junshan Xie

    (Henan University)

Abstract

In this paper, we study the efficient robust estimation and empirical likelihood for a single-index mixed effects model with a subset of covariates and response missing at random. Three efficient robust estimators and empirical likelihood ratios for index coefficients are constructed using weighted, imputed and weighted-imputed method, their asymptotic properties are proved. Our results show that the three estimators are asymptotically equivalent, and a weighted-imputed empirical log-likelihood ratio is asymptotically chi-squared. An important feature of our methods is their ability to handle missing response and/or partially missing covariates. Some simulation studies and a real data example indicate that our methods have fine performance in finite sample, and are available in practice.

Suggested Citation

  • Liugen Xue & Junshan Xie, 2024. "Efficient robust estimation for single-index mixed effects models with missing observations," Statistical Papers, Springer, vol. 65(2), pages 827-864, April.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:2:d:10.1007_s00362-023-01407-2
    DOI: 10.1007/s00362-023-01407-2
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    References listed on IDEAS

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    1. Pang, Zhen & Xue, Liugen, 2012. "Estimation for the single-index models with random effects," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1837-1853.
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    3. Ying Wei & Yanyuan Ma & Raymond J. Carroll, 2012. "Multiple imputation in quantile regression," Biometrika, Biometrika Trust, vol. 99(2), pages 423-438.
    4. Xue, Liugen & Zhang, Jinghua, 2020. "Empirical likelihood for partially linear single-index models with missing observations," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    5. Qin, Jing & Zhang, Biao & Leung, Denis H. Y., 2009. "Empirical Likelihood in Missing Data Problems," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1492-1503.
    6. Masry, Elias & Tjøstheim, Dag, 1995. "Nonparametric Estimation and Identification of Nonlinear ARCH Time Series Strong Convergence and Asymptotic Normality: Strong Convergence and Asymptotic Normality," Econometric Theory, Cambridge University Press, vol. 11(2), pages 258-289, February.
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    Cited by:

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    2. Qian Sun & Yang Zhou & Shouyou Huang, 2025. "Fast rates of exponential cost function," Statistical Papers, Springer, vol. 66(3), pages 1-19, April.

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