Shrinkage estimates of small domain parameters typically utilize a combination of a noisy "direct" estimate that only uses data from a specific small domain and a more stable regression estimate. When the regression model is misspecified, estimation performance for the noisier domains can suffer due to substantial shrinkage towards a poorly estimated regression surface. In this paper, we introduce a new class of robust, empirically-driven regression weights that target estimation of the small domain means under potential misspecification of the global regression model. Our regression weights are a convex combination of the model-based weights associated with the best linear unbiased predictor (BLUP) and those associated with the observed best predictor (OBP). The compromise parameter in this convex combination is found by minimizing a novel, unbiased estimate of the mean-squared prediction error for the small domain means, and we label the associated small domain estimates the "compromise best predictor", or CBP. Using a data-adaptive mixture for the regression weights enables the CBP to possess the robustness of the OBP while retaining the main advantages of the EBLUP whenever the regression model is correct. We demonstrate the use of the CBP in an application estimating gait speed in older adults.
翻译:微小域参数的缩小估计通常使用噪音的“ 直接” 估计组合,该估计只使用特定小域的数据和较稳定的回归估计。当回归模型定义错误时,由于向低估计回归表面的大幅缩小,对音响域的性能估计可能会受到影响。在本文中,我们引入了新型的稳健的、经验驱动的回归加权值,以在全球回归模型可能误差的情况下对小域值进行目标估计。我们的回归加权值是模型基重的组合,它与最佳线性预测仪(BLUP)和观察到的最佳预测仪(OBP)相关联。这一曲线组合的折中参数是通过尽量减少对小域值手段的中度预测错误的新的、不偏差估计而发现的。我们将相关的小域估计值标为“最精确的预测仪”或CBP。使用数据适应性混合值使CBP能够拥有以模型为基础的稳健性,同时保留EBLUP的主要优势,只要回归模型在更老的成人中进行估计。我们用CBP模型来证明。