Subsample-Based Estimation under Dynamic Contamination

TL;DR

This paper reveals a fundamental failure of subsample-based estimators in dynamic time series models under contamination, and proposes a transformation to restore consistency without modeling contamination.

Contribution

It identifies a structural incompatibility in subsampling methods under contamination and introduces a propagation-compatible transformation to ensure estimator consistency.

Findings

Subsample-based estimators are inconsistent under contamination in dynamic models.

A transformation based on patch removal restores estimator consistency.

The approach applies broadly to residual-based estimators without modeling contamination.

Abstract

This paper studies a structural failure of subsample-based estimation in dynamic time series models. Even under oracle knowledge of contamination locations, removing contaminated observations does not restore the uncontaminated objective. In such settings, contamination propagates through the residual filter and distorts the estimation criterion. As a result, subsample-based estimators are generically inconsistent for the clean-data parameter. We characterise this failure as a structural incompatibility between pointwise subsampling and residual propagation. More generally, the failure arises whenever contamination propagates through transformations that enter the estimation criterion, with dynamic time series models as a leading example. To address it, we propose a propagation-compatible transformation of index sets via a patch removal operator. Under general high-level conditions, this transformation leaves the estimator asymptotically unchanged under the uncontaminated model while restoring consistency under contamination. The results apply to a broad class of residual-based estimators and do not rely on modelling the contamination process.