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非线性混合模型中小区域预测均方误差的刀切估计AI 解读

Empirical Bayes predictors of small area parameters of interest are often obtained under a linear mixed model for continuous response data or a generalized linear mixed model for binary responses or count data. However, estimation of the unconditional mean squared error of prediction is complicated, particularly for a nonlinear mixed model. Jiang et al. (2002) proposed a jackknife method for estimating the unconditional mean squared error and showed that the resulting…

辅助信息含测量误差时的小区域估计AI 解读

Small area estimation methods typically combine direct estimates from a survey with predictions from a model in order to obtain estimates of population quantities with reduced mean squared error. When the auxiliary information used in the model is measured with error, using a small area estimator such as the Fay--Herriot estimator while ignoring measurement error may be worse than simply using the direct estimator. We propose a new small area estimator that accounts for…

单因素随机效应模型的最优贝叶斯实验设计AI 解读

Since variance components are nonlinear parameters in a linear model, classical optimal designs for estimating variance components in the one-way random effects model depend on the values of the parameters. Optimal Bayesian designs are derived for the more realistic situation of unknown parameters, using the Fisher information of the variance components as a basis for comparing the designs. Balanced designs, in which the same number of measurements are taken on each unit,…