arXiv 20 Apr 2026 · Statistics — Methodology
arXiv:2604.17676 · PDF · DOI · OpenAlex · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Johansen, Søren and Nielsen, Bent (2016) Asymptotic Theory of Outlier Detection Algorithms for Linear Time Series Regression Models | 1.000 | 6 | 4 | 100% |
| 2 | Huber, Peter J (1964) Robust Estimation of a Location Parameter | 1.000 | 5 | 3 | 100% |
| 3 | Peter J. Rousseeuw (1984) Least Median of Squares Regression | 1.000 | 5 | 3 | 100% |
| 4 | Søren Johansen and Bent Nielsen (2009) An analysis of the indicator saturation estimator as a robust regression estimator | 0.843 | 3 | 3 | 100% |
| 5 | Maronna, Ricardo A. and Martin, R. Douglas and Yohai, Victor J (2006) Robust Statistics: Theory and Methods | 0.843 | 3 | 3 | 100% |
| 6 | Chang, Ih and Tiao, George C. and Chen, Chung (1988) Estimation of Time Series Parameters in the Presence of Outliers | 0.737 | 3 | 2 | 100% |
| 7 | Fox, A. J (1972) Outliers in Time Series | 0.737 | 3 | 2 | 100% |
| 8 | Atkinson, Anthony C. and Riani, Marco (2000) Robust Diagnostic Regression Analysis | 0.644 | 2 | 2 | 100% |
| 9 | Hadi, Ali S. and Simonoff, Jeffrey S (1993) Procedures for the Identification of Multiple Outliers in Linear Models | 0.644 | 2 | 2 | 100% |
| 10 | Johansen, Søren and Nielsen, Bent (2013) Outlier Detection in Regression Using an Iterated One-Step Approximation to the Huber-Skip Estimator | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 42 scored citations.