Semiparametric Efficient Data Integration Using the Dual-Frame Sampling Framework

TL;DR

This paper develops semiparametric methods for integrating probability and non-probability samples, providing efficient estimators that work under unknown sampling mechanisms and are robust to misspecification, with practical implementation in R.

Contribution

It introduces two novel estimators for dual-frame data integration, one achieving the semiparametric efficiency bound and the other offering robustness without explicit modeling.

Findings

The parametric estimator attains the semiparametric efficiency bound.

The second estimator is robust to model misspecification.

Simulations demonstrate efficiency gains and stable performance.

Abstract

Integrating probability and non-probability samples is increasingly important, yet unknown sampling mechanisms in non-probability sources complicate identification and efficient estimation. We develop semiparametric theory for dual-frame data integration and propose two complementary estimators. The first models the non-probability inclusion probability parametrically and attains the semiparametric efficiency bound. We introduce an identifiability condition based on strong monotonicity that identifies sampling-model parameters without instrumental variables, even under informative (non-ignorable) selection, using auxiliary information from the probability sample; it remains valid without record linkage between samples. The second estimator, motivated by a two-stage sampling approximation, avoids explicit modeling of the non-probability mechanism; though not fully efficient, it is efficient within a restricted augmentation class and is robust to misspecification. Simulations and an application to the Culture and Community in a Time of Crisis public simulation dataset show efficiency gains under correct specification and stable performance under misspecification and weak identification. Methods are implemented in the R package \texttt{dfSEDI}.