Is External Information Useful for Data Fusion? An Evaluation before Acquisition

TL;DR

This paper introduces a method to evaluate the potential benefit of external information for data fusion using internal data alone, enabling cost-effective decisions on acquiring external data before actual collection.

Contribution

It proposes a universal utility measure based on efficiency bounds and a methodology to estimate it using only internal data, applicable across various external information types.

Findings

The utility measure accurately predicts efficiency gains from external data.

The proposed estimators have proven asymptotic properties.

Simulation and real data demonstrate practical effectiveness.

Abstract

We consider a general statistical estimation problem involving a finite-dimensional target parameter vector. Beyond an internal data set drawn from the population distribution, external information, such as additional individual data or summary statistics, can potentially improve the estimation when incorporated via appropriate data fusion techniques. However, since acquiring external information often incurs costs, it is desirable to assess its utility beforehand using only the internal data. To address this need, we introduce a utility measure based on estimation efficiency, defined as the ratio of semiparametric efficiency bounds for estimating the target parameters with versus without incorporating the external information. It quantifies the maximum potential efficiency improvement offered by the external information, independent of specific estimation methods. To enable inference on this measure before acquiring the external information, we propose a general approach for constructing its estimators using only the internal data, adopting the efficient influence function methodology. Several concrete examples, where the target parameters and external information take various forms, are explored, demonstrating the versatility of our general framework. For each example, we construct point and interval estimators for the proposed measure and establish their asymptotic properties. Simulation studies confirm the finite-sample performance of our approach, while a real data application highlights its practical value. In scientific research and business applications, our framework significantly empowers cost-effective decision making regarding acquisition of external information.