Assumption-Lean Shrinkage and Model Averaging for Spatial Parameters
弱模型依赖的空间参数收缩与模型平均AI 解读 ↓
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弱模型依赖的空间参数收缩与模型平均AI 解读 ↓
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Economic decisions often depend on many noisy estimates of quantities such as neighborhood effects, school quality, and hospital performance. Shrinkage estimation can improve decisions by pooling information across related units, but geography, adjacency, and shared characteristics each define a different notion of relatedness, and each implies a different way of pooling. We treat the choice of relatedness as part of the estimation problem, using Stein's Unbiased Risk Estimate (SURE) to form a weighted average over a library of flexible shrinkage estimators. This comparison among the candidate estimators treats no prior or latent covariance structure as a correctly specified model for the parameters being estimated. Each candidate is judged by its SURE value. Under smoothness conditions on the estimators, the SURE-weighted average performs nearly as well as the best fixed weighted average of trained candidates, including nonlinear rules whose reported values use the full vector of noisy estimates. In an application to Opportunity Atlas economic mobility data from 20 commuting zones, the best individual spatial specification varies across zones, yet the SURE-weighted average tracks the best in each zone and reduces estimated mean squared error by about 27% relative to the best-performing non-spatial empirical Bayes baseline in our library of estimators.
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With the advance of measurement technologies and increasing computing power, large spatial data with heterogeneous structures are often collected over high-dimensional domains. Existing Gaussian process (GP) models and computational strategies are often inadequate for analyzing such datasets in multi-dimensional domains. To address these challenges, we develop a Bayesian residual tree GP methodology called ResTGP for large spatial data with potentially heterogeneous…
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图分割贝叶斯因果森林:空间异质性处理效应估计
In spatial observational studies, treatment assignment and outcomes often exhibit spatial dependence patterns, and treatment effects may vary across space and subpopulations due to both measured and unmeasured spatially structured confounders. Accounting for spatial dependence while estimating heterogeneous treatment effects (HTEs) is a central task in spatial causal inference. Causal Bayesian additive regression tree methods are popular nonparametric methods for modeling…