Multi-source Learning for Target Population by High-dimensional Calibration

TL;DR

This paper introduces a high-dimensional calibration method for multi-source learning that effectively combines heterogeneous datasets to estimate target population parameters with improved efficiency and robustness.

Contribution

It proposes a novel high-dimensional debiased calibration (HDC) method and a multi-source HDC (MHDC) estimator that support flexible models and enhance efficiency in multi-source data integration.

Findings

MHDC estimator achieves asymptotic normality.

It outperforms existing doubly robust estimators in simulations.

The method demonstrates practical utility in meteorological data analysis.

Abstract

Multi-source learning is an emerging area of research in statistics, where information from multiple datasets with heterogeneous distributions is combined to estimate the parameter of interest for a target population without observed responses. We propose a high-dimensional debiased calibration (HDC) method and a multi-source HDC (MHDC) estimator for general estimating equations. The HDC method uses a novel approach to achieve Neyman orthogonality for the target parameter via high-dimensional covariate balancing on an augmented set of covariates. It avoids the augmented inverse probability weighting formulation and leads to an easier optimization algorithm for the target parameter in estimating equations and M-estimation. The proposed MHDC estimator integrates multi-source data while supporting flexible specifications for both density ratio and outcome regression models, achieving multiple robustness against model misspecification. Its asymptotic normality is established, and a specification test is proposed to examine the transferability condition for the multi-source data. Compared to the linear combination of single-source HDC estimators, the MHDC estimator improves efficiency by jointly utilizing all data sources. Through simulation studies, we show that the MHDC estimator accommodates multiple sources and multiple working models effectively and performs better than the existing doubly robust estimators for multi-source learning. An empirical analysis of a meteorological dataset demonstrates the utility of the proposed method in practice.