How estimating nuisance parameters can reduce the variance (with consistent variance estimation).

ABSTRACT: We often estimate a parameter of interest ψ$$ \psi $$ when the identifying conditions involve a finite-dimensional nuisance parameter θ∈ℝd$$ \theta \in {\mathbb{R}}^d $$ . Examples from causal inference are inverse probability weighting, marginal structural models and structural nested models, which all lead to unbiased estimating equations. This article presents a consistent sandwich estimator for the variance of estimators ψ^$$ \hat{\psi} $$ that solve unbiased estimating equations including θ$$ \theta $$ which is also estimated by solving unbiased estimating equations. This article presents four additional results for settings where θ^$$ \hat{\theta} $$ solves (partial) score equations and ψ$$ \psi $$ does not depend on θ$$ \theta $$ . This includes many causal inference settings where

SUBMITTER: Lok JJ 

PROVIDER: S-EPMC11570876 | biostudies-literature | 2024 Oct

REPOSITORIES: biostudies-literature