Semiparametric Efficient Inference under Non-Informative Complex Survey Designs

2026-09-15

AI Summary

该研究解决了复杂抽样设计下的半参数有效推断问题，通过局部渐近正态性和参考泊松实验的切空间结构方法来处理设计诱导的依赖性和有限总体目标的随机性。

Abstract

Two features intrinsic to survey sampling complicate semiparametric efficiency analysis: design-induced dependence among sampling indicators and the randomness of finite-population targets under the superpopulation law. For general semiparametric full-data models, we show that the observed-data experiment under a broad class of dependent designs is locally asymptotically normal with the tangent-space structure of a reference Poisson experiment. Under the joint superpopulation-design law, first-order efficiency depends on the design only through the limiting inclusion-probability function. Standard missing-at-random projection in the reference experiment characterizes the observed-data efficient influence function. Finite-population targets are treated through first-order asymptotic expansions, extending the analysis beyond exact random sums to nonlinear census characteristics. Superpopulation and finite-population centerings yield equivalent notions of local regularity and efficiency, with their bounds linked by a Pythagorean decomposition that gives a generalized finite-population correction. We then give general and design-specific conditions under which cross-fitted estimators with estimated nuisance functions attain both efficiency bounds. For the finite-population mean, the bound equals the large-sample limit of the Godambe-Joshi anticipated-variance lower bound. For scalar targets, we characterize optimal limiting inclusion probabilities. Simulations and California Academic Performance Index data illustrate the theory.

Problem

• semiparametric efficiency
• complex survey designs
• sampling dependence
• finite-population targets

Innovation

• semiparametric efficiency
• complex survey designs
• Poisson experiment
• influence function
• finite-population correction