论文标题
替代均方根误差估计器和置信区间，用于预测非线性小面积参数
Alternative Mean Square Error Estimators and Confidence Intervals for Prediction of Nonlinear Small Area Parameters
论文作者
论文摘要
MSE估计的困难之所以发生，是因为我们没有为调查权重指定完整分布。这混淆了完全参数的引导程序。为了克服这一挑战，我们开发了一种新颖的MSE估计器。我们使用用于构造基本预测变量的相同模拟样本，估计MSE中的主要术语（是最佳预测指标的MSE（用真实参数构建）。然后，我们利用参数估计器的渐近正态分布来估计MSE中的第二项，这反映了估计参数的可变性。我们在不使用计算密集的双重引导程序的情况下对估计器的估计器的偏置进行了校正。我们进一步开发了校准的预测间隔，这些预测间隔依赖于正常理论而不是标准预测间隔。我们通过广泛的模拟研究从经验上证明了所提出的程序的有效性。我们应用了使用复杂的农业调查的数据来预测爱荷华州的几种床单和RILL侵蚀功能。
A difficulty in MSE estimation occurs because we do not specify a full distribution for the survey weights. This obfuscates the use of fully parametric bootstrap procedures. To overcome this challenge, we develop a novel MSE estimator. We estimate the leading term in the MSE, which is the MSE of the best predictor (constructed with the true parameters), using the same simulated samples used to construct the basic predictor. We then exploit the asymptotic normal distribution of the parameter estimators to estimate the second term in the MSE, which reflects variability in the estimated parameters. We incorporate a correction for the bias of the estimator of the leading term without the use of computationally intensive double-bootstrap procedures. We further develop calibrated prediction intervals that rely less on normal theory than standard prediction intervals. We empirically demonstrate the validity of the proposed procedures through extensive simulation studies. We apply the methods to predict several functions of sheet and rill erosion for Iowa counties using data from a complex agricultural survey.
