Asymptotics for EBLUPs: Nested Error Regression Models
Asymptotics for EBLUPs: Nested Error Regression Models
复制标题
EBLUP 的渐进：嵌套误差回归模型
DOI：
10.1080/01621459.2021.1895178
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发表时间：
2021
影响因子：
3.7
通讯作者：
Alan H. Welsh
中科院分区：
文献类型：
--
作者：
Ziyang Lyu;Alan H. Welsh
本文给出了嵌套误差回归模型中随机效应的估计最佳线性无偏预报器(EBLUP)的渐近分布。在不要求正态分布的非常温和的条件下，我们证明了当团簇数目和团簇大小都发散到无穷大时，EBLUP的分布是随机效应的真实分布和正态分布的卷积。这一结果给出了EBLUP的预测均方误差的非常简单的渐近逼近和估计量，然后给出了未观察到的随机效应的渐近预测区间。我们还推导了渐近均方误差的高阶近似，并与Kackar和Harville以及Prasad和Rao提出的著名的分析预测均方误差近似和估计量进行了详细的理论和经验比较。我们证明了当簇的数目和簇的大小都足够大时，我们对EBLUP的预测均方误差的简单估计器在实践中工作得很好。最后，我们用马萨诸塞州和亚利桑那州的房屋测氡数据说明了渐近预测区间的使用。
Abstract In this article we derive the asymptotic distribution of estimated best linear unbiased predictors (EBLUPs) of the random effects in a nested error regression model. Under very mild conditions which do not require the assumption of normality, we show that asymptotically the distribution of the EBLUPs as both the number of clusters and the cluster sizes diverge to infinity is the convolution of the true distribution of the random effects and a normal distribution. This result yields very simple asymptotic approximations to and estimators of the prediction mean squared error of EBLUPs, and then asymptotic prediction intervals for the unobserved random effects. We also derive a higher order approximation to the asymptotic mean squared error and provide a detailed theoretical and empirical comparison with the well-known analytical prediction mean squared error approximations and estimators proposed by Kackar and Harville and Prasad and Rao. We show that our simple estimator of the predictor mean squared errors of EBLUPs works very well in practice when both the number of clusters and the cluster sizes are sufficiently large. Finally, we illustrate the use of the asymptotic prediction intervals with data on radon measurements of houses in Massachusetts and Arizona.