Improved Small Domain Estimation via Compromise Regression Weights

• 成果类型: Article
• 署名作者: Henderson, Nicholas C.; Varadhan, Ravi; Louis, Thomas A.
• 署名单位: University of Michigan System; University of Michigan; Johns Hopkins University; Johns Hopkins Medicine; Johns Hopkins University; Johns Hopkins Bloomberg School of Public Health
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2022.2080682
• 发表日期: 2023
• 页码: 2793-2809
• 关键词: walking speed; prediction; models

摘要

Shrinkage estimates of small domain parameters typically use 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 toward a poorly estimated regression surface. In this article, 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 mixing 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 preserve 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. Supplementary materials for this article are available online.