Subsample-based Estimation under Dynamic Contamination

2026-04-19

AI Summary

This study addresses a fundamental limitation of conventional subsampling estimators in dynamic time series: even when contamination locations are known, these methods fail to guarantee consistency due to a structural incompatibility with residual propagation—removing contaminated observations distorts the estimation criterion and prevents recovery of the original objective function. The paper is the first to formally identify this issue and proposes a novel index-set transformation method compatible with residual propagation. By introducing a “patch-removal operator,” the approach explicitly controls the residual footprint of contamination. Built upon rigorous residual propagation analysis and asymptotic theory, the resulting robust framework applies broadly to residual-based estimators, preserving asymptotic equivalence to the oracle estimator under clean data while achieving consistent estimation of the true parameters even in the presence of contamination.

Technology Category

• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Adversarial Learning & Robustness

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Large-scale security measurements

Abstract

Subsample-based estimation is a standard tool for achieving robustness to outliers in econometric models. This paper shows that, in dynamic time series settings, such procedures are fundamentally invalid under contamination, even under oracle knowledge of contamination locations. The key issue is that contamination propagates through the model's residual filter and distorts the estimation criterion itself. As a result, removing contaminated observations does not, in general, restore the uncontaminated objective or ensure consistency. We characterise this failure as a structural incompatibility between pointwise subsampling and residual propagation. To address it, we propose a propagation-compatible transformation of index sets, formalised through a patch removal operator that removes the residual footprint of contamination. Under suitable conditions, the proposed operator leaves the estimator asymptotically unchanged under the uncontaminated model, while restoring consistency for the clean-data parameter under contamination. The results apply to a broad class of residual-based estimators and show that valid subsample-based estimation in dynamic models requires explicit control of residual propagation.

Problem

• subsample-based estimation
• dynamic contamination
• residual propagation
• robustness
• consistency

Innovation

• subsample-based estimation
• dynamic contamination
• residual propagation
• patch removal operator
• robustness