Improving prediction in M-estimation by integrating external information from heterogeneous populations

2025-09-04

AI Summary

This paper addresses the limited predictive and inferential performance of M-estimation in heterogeneous populations. To overcome this, we propose a novel shrinkage estimation method that integrates external heterogeneous data. By constructing a joint asymptotic framework, our approach jointly models internal data with external data that provide partial prior information on parameters. We introduce a class of generalized parameter transformations to consistently aggregate estimates from multiple heterogeneous sources, ensuring cross-population statistical consistency while substantially improving estimation stability and accuracy. Theoretically, the estimator is proven to be asymptotically optimal under mild regularity conditions. Numerical experiments demonstrate that the proposed method outperforms existing approaches in estimation efficiency, prediction accuracy, and robustness—particularly under model misspecification and data heterogeneity. Our work thus provides a scalable theoretical framework and practical methodology for robust inference with multi-source heterogeneous data.

Technology Category

• Machine Learning: Ensemble Methods
• Intelligent Robots: State Estimation
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

A novel approach to improve prediction and inference in M-estimation by integrating external information from heterogeneous populations is proposed. Our method leverages joint asymptotics to combine estimates from external and internal datasets, where the external dataset provides auxiliary information about a subset of parameters of interest. We introduce a shrinkage estimator that combines internal and external estimates under a general class of transformations that ensure consistency across populations.

Problem

• Integrating external data from heterogeneous populations
• Improving prediction and inference in M-estimation
• Developing shrinkage estimator for parameter consistency

Innovation

• Integrating external information from heterogeneous populations
• Leveraging joint asymptotics to combine estimates
• Introducing shrinkage estimator under general transformations