Influence Functions for LTS and Reweighted LTS Estimators Based on Moment Condition

Verardi, Vincenzo;Jann, Ben;Vermandele, Catherine
(2026) Statistics & Probability Letters — (2026)

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Abstract
The Least Trimmed Squares (LTS) regression estimator, introduced by Rousseeuw (1984), minimizes the sum of the ⌈αn⌉ smallest squared residuals (generally 50% of the observations), providing a robust-to-outliers alternative to ordinary least squares. Interestingly, in the case of i.i.d. error terms, this estimator can also be written as a solution to an exactly identified Generalized Method of Moments (GMM) problem. Applying standard GMM theory, the influence function and asymptotic variance can be easily derived by computing moment conditions and their derivatives. The moment-based approach also provides the influence function for a one-step adaptive reweighted estimator as proposed by Cızek (2013).
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Verardi, V., Jann, B., & Vermandele, C. (2026). Influence Functions for LTS and Reweighted LTS Estimators Based on Moment Condition. Statistics & Probability Letters. Accepted/in-press. https://hdl.handle.net/2078.5/272565 (Original work published 2026)