Doubly Robust and Locally Efficient Estimation with Missing Outcomes
نویسندگان
چکیده
We consider parametric regression where the outcome is subject to missingness. To achieve the semiparametric efficiency bound, most existing estimation methods require the correct modeling of certain second moments of the data, which can be very challenging in practice. We propose an estimation procedure based on the conditional empirical likelihood (CEL) method. Our method does not require us to model any second moments. We study the CEL-based inverse probability weighted (CEL-IPW) and augmented inverse probability weighted (CEL-AIPW) estimators in detail. Under some regularity conditions and the missing at random (MAR) mechanism, the CEL-IPW estimator is consistent if the missingness mechanism is correctly modeled, and the CEL-AIPW estimator is consistent if either the missingness mechanism or the conditional mean of the outcome is correctly modeled. When both quantities are correctly modeled, the CEL-AIPW estimator attains the semiparametric efficiency bound without modeling any second moments. The asymptotic distributions are derived. Numerical implementation through nested optimization routines using the Newton-Raphson algorithm is discussed.
منابع مشابه
Estimation and inference based on Neumann series approximation to locally efficient score in missing data problems.
Theory on semiparametric efficient estimation in missing data problems has been systematically developed by Robins and his coauthors. Except in relatively simple problems, semiparametric efficient scores cannot be expressed in closed forms. Instead, the efficient scores are often expressed as solutions to integral equations. Neumann series was proposed in the form of successive approximation to...
متن کاملBounded , efficient and doubly robust estimation with inverse weighting
Consider estimating the mean of an outcome in the presence of missing data or estimating population average treatment effects in causal inference. A doubly robust estimator remains consistent if an outcome regression model or a propensity score model is correctly specified. We build on a previous nonparametric likelihood approach and propose new doubly robust estimators, which have desirable pr...
متن کاملBounded, Efficient, and Doubly Robust Estimation with Inverse Weighting
Consider the problem of estimating the mean of an outcome in the presence of missing data or estimating population average treatment effects in causal inference. A doubly robust estimator remains consistent if an outcome regression model or a propensity score model is correctly specified. We build on the nonparametric likelihood approach of Tan and propose new doubly robust estimators. These es...
متن کاملCross-Fitting and Fast Remainder Rates for Semiparametric Estimation
There are many interesting and widely used estimators of a functional with finite semiparametric variance bound that depend on nonparametric estimators of nuisance functions. We use cross-fitting (i.e. sample splitting) to construct novel estimators with fast remainder rates. We give cross-fit doubly robust estimators that use separate subsamples to estimate different nuisance functions. We obt...
متن کاملOn L convergence of Neumann series approximation in missing data problems.
The inverse of the nonparametric information operator is key to finding doubly robust estimators and the semiparametric efficient estimator in missing data problems. It is known that no closed-form expression for the inverse of the nonparametric information operator exists when missing data form nonmonotone patterns. Neumann series is usually applied to approximate the inverse. However, Neumann...
متن کامل