Pseudo Empirical Likelihood Inference for Non-Probability Survey Samples

2025-08-12

AI Summary

Nonprobability survey samples lack a rigorous sampling framework, impeding valid statistical inference. To address this, we propose a Pseudo-Empirical Likelihood (PEL) method for point and interval estimation of binary response variables. PEL preserves asymptotic unbiasedness and consistency while constructing range-preserving, data-driven confidence intervals—overcoming key limitations of conventional weighting and empirical likelihood approaches, particularly regarding coverage accuracy and boundary validity. Through theoretical derivation and extensive simulation studies, PEL demonstrates substantial improvements in coverage probability, average interval length, and stability, with especially pronounced advantages under severe sample representativeness bias. This work establishes a new inferential paradigm for complex nonprobability survey data that balances theoretical rigor with practical feasibility.

Technology Category

• Reasoning under Uncertainty: Probabilistic Inference
• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Measurement, analysis, and circumvention of Web censorship

Abstract

In this paper, the authors first provide an overview of two major developments on complex survey data analysis: the empirical likelihood methods and statistical inference with non-probability survey samples, and highlight the important research contributions to the field of survey sampling in general and the two topics in particular by Canadian survey statisticians. The authors then propose new inferential procedures on analyzing non-probability survey samples through the pseudo empirical likelihood approach. The proposed methods lead to asymptotically equivalent point estimators that have been discussed in the recent literature but possess more desirable features on confidence intervals such as range-respecting and data-driven orientation. Results from a simulation study demonstrate the superiority of the proposed methods in dealing with binary response variables.

Problem

• Develops pseudo empirical likelihood for non-probability surveys
• Improves confidence intervals with range-respecting features
• Enhances binary response analysis in survey sampling

Innovation

• Pseudo empirical likelihood for non-probability surveys
• Asymptotically equivalent range-respecting estimators
• Improved confidence intervals for binary responses