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Parametric bootstrap methods for bias correction in linear mixed models

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  • Kubokawa, Tatsuya
  • Nagashima, Bui

Abstract

The empirical best linear unbiased predictor (EBLUP) in the linear mixed model (LMM) is useful for the small area estimation, and the estimation of the mean squared error (MSE) of EBLUP is important as a measure of uncertainty of EBLUP. To obtain a second-order unbiased estimator of the MSE, the second-order bias correction has been derived based on Taylor series expansions. However, this approach is hard to implement in complicated models with many unknown parameters like variance components, since we need to compute asymptotic bias, variance and covariance for estimators of unknown parameters as well as partial derivatives of some quantities. A similar difficulty occurs in the construction of confidence intervals based on EBLUP with second-order correction and in the derivation of second-order bias correction in the Akaike Information Criterion (AIC) and the conditional AIC. To avoid such difficulty in the derivation of second-order bias correction in these problems, the parametric bootstrap methods are suggested in this paper, and their second-order justifications are established. Finally, performances of the suggested procedures are numerically investigated in comparison with some existing procedures given in the literature.

Suggested Citation

  • Kubokawa, Tatsuya & Nagashima, Bui, 2012. "Parametric bootstrap methods for bias correction in linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 106(C), pages 1-16.
    • Handle: RePEc:eee:jmvana:v:106:y:2012:i:c:p:1-16
    DOI: 10.1016/j.jmva.2011.12.002
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    References listed on IDEAS

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    10. Kubokawa, Tatsuya, 2011. "Conditional and unconditional methods for selecting variables in linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 641-660, March.
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    Cited by:

    1. Yuki Kawakubo & Shonosuke Sugasawa & Tatsuya Kubokawa, 2014. "Conditional AIC under Covariate Shift with Application to Small Area Prediction," CIRJE F-Series CIRJE-F-944, CIRJE, Faculty of Economics, University of Tokyo.
    2. Kawakubo, Yuki & Kubokawa, Tatsuya, 2014. "Modified conditional AIC in linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 44-56.
    3. Tatsuya Kubokawa, 2012. "Mixed Effects Prediction under Benchmarking and Applications to Small Area Estimation," CIRJE F-Series CIRJE-F-832, CIRJE, Faculty of Economics, University of Tokyo.
    4. Flores-Agreda, Daniel & Cantoni, Eva, 2019. "Bootstrap estimation of uncertainty in prediction for generalized linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 130(C), pages 1-17.
    5. Yuki Kawakubo & Tatsuya Kubokawa, 2013. "Modfiied Conditional AIC in Linear Mixed Models," CIRJE F-Series CIRJE-F-895, CIRJE, Faculty of Economics, University of Tokyo.

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