Parametric bootstrap methods for bias correction in linear mixed models

Tatsuya Kubokawa and Bui Nagashima

Journal of Multivariate Analysis, 2012, vol. 106, issue C, 1-16

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.

Keywords: Best linear unbiased predictor; Confidence interval; Empirical Bayes procedure; Fay–Herriot model; Second-order correction; Linear mixed model; Maximum likelihood estimator; Mean squared error; Nested error regression model; Parametric bootstrap; Restricted maximum likelihood estimator; Small area estimation (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (5)

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DOI: 10.1016/j.jmva.2011.12.002

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