Functional Estimation under Proxy-Based Full-Law Identification

2026-09-14

AI Summary

本文通过利用与未观测变量相关的代理变量，提出了在存在潜在变量情况下识别完整数据律的一般条件，并使用基于代理的加权方案开发了估计方程。

Abstract

We state general conditions under which the full-data law is identified in the presence of latent variables, leveraging key observed variables ("proxies") associated with unobserved variables. These assumptions extend those used in existing examples from the literature that recover the full-data law under relatively flexible model assumptions. We first describe graphical models compatible with our assumptions, and then consider target parameters that are functionals of the full-data law, developing estimating equations that give rise to consistent M-estimators using the observed data. Our approach replaces unobserved random variables appearing in full-data estimating equations with observed variables via a proxy-based weighting scheme. This strategy can be extended to construct observed-data influence functions, giving estimators with desirable properties such as multiple robustness and \(\sqrt{n}\)-consistency despite slower than parametric convergence of nuisance functions.

Problem

• latent variables
• proxies
• full-data law
• graphical models
• M-estimators

Innovation

• proxy-based weighting scheme
• full-data law identification
• observed-data influence functions
• multiple robustness