Bias Robust Estimation in Finite Populations Using Nonparametric Calibration

Abstract

A Standard problem in sample survey inference is that of predicting the finite population total H of a function h(y) of a random variable Y. The model-based approach to this problem first defines a working model ξ for Y and then predicts H by estimating its expectation under ξ, conditional on the sample values of Y. This approach leads to biased predictions if ξ is incorrect. We explore an automatic solution to this misspecification bias that uses nonparametric regression to define a robust (but inefficient) predictor of H, and then calibrates this predictor for its bias under ξ. An application to prediction of the finite population distribution function of a population of Australian beef farms is presented.