Model Averaging Methods for Weight Trimming

In sample surveys where sampled units have unequal probabilities of inclusion, associations between the inclusion probabilities and the statistic of interest can induce bias. Weights equal to the inverse of the probability of inclusion are often used to counteract this bias. Highly disproportional sample designs have highly variable weights, which can introduce undesirable variability in statistics such as the population mean or linear regression estimates. Weight trimming reduces large weights to a fixed maximum value, reducing variability but introducing bias. Most standard approaches are ad-hoc in that they do not use the data to optimize bias-variance tradeoffs. This manuscript develops variable selection models, termed "weight pooling" models, that extend weight trimming procedures in a Bayesian model averaging framework to produce "data driven" weight trimming estimators. We develop robust yet efficient models that approximate fully-weighted estimators when bias correction is of greatest importance, and approximate unweighted estimators when variance reduction is critical.