Parametric bootstrap approximation to the distribution of EBLUP and related prediction intervals in linear mixed models
Parametric bootstrap approximation to the distribution of EBLUP and related prediction intervals in linear mixed models
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DOI：
10.1214/07-aos512
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发表时间：
2008-06-01
影响因子：
4.5
通讯作者：
Li, Huilin
中科院分区：
文献类型：
--
作者：
Chatterjee, Snigdhansu;Lahiri, Partha;Li, Huilin
经验最佳线性无偏预测（EBLUP）方法使用线性混合模型来组合来自不同信息源的信息。这种方法在小面积问题中特别有用。EBLUP的变异性传统上由均方预测误差（MSPE）来衡量，区间估计通常使用MSPE的估计来构建。这些方法存在覆盖不足或过度覆盖、长度过长和缺乏可解释性等缺点。我们提出了一个参数引导的方法来估计一个适当的集中和缩放EBLUP的整个分布。Bootstrap直方图是高度精确的，与真实的EBLUP分布的差异仅为O（d（3）n（-3/2）），其中d是参数的数量，n是观测的数量。该结果用于获得高精度的预测区间。仿真结果表明，该方法优于现有的线性混合模型的预测区间构造技术。
Empirical best linear unbiased prediction (EBLUP) method uses a linear mixed model in combining information from different sources of information. This method is particularly useful in small area problems. The variability of an EBLUP is traditionally measured by the mean squared prediction error (MSPE), and interval estimates are generally constructed using estimates of the MSPE. Such methods have shortcomings like under-coverage or over-coverage, excessive length and lack of interpretability. We propose a parametric bootstrap approach to estimate the entire distribution of a suitably centered and scaled EBLUP. The bootstrap histogram is highly accurate, and differs from the true EBLUP distribution by only O(d(3)n(-3/2)), where d is the number of parameters and n the number of observations. This result is used to obtain highly accurate prediction intervals. Simulation results demonstrate the superiority of this method over existing techniques of constructing prediction intervals in linear mixed models.