Robust direction estimation in single-index models via cumulative divergence

Shuaida He, Jiarui Zhang and Xin Chen

Computational Statistics & Data Analysis, 2025, vol. 202, issue C

Abstract: In this paper, we address direction estimation in single-index models, with a focus on heavy-tailed data applications. Our method utilizes cumulative divergence to directly capture the conditional mean dependence between the response variable and the index predictor, resulting in a model-free property that obviates the need for initial link function estimation. Furthermore, our approach allows heavy-tailed predictors and is robust against the presence of outliers, leveraging the rank-based nature of cumulative divergence. We establish theoretical properties for our proposal under mild regularity conditions and illustrate its solid performance through comprehensive simulations and real data analysis.

Keywords: Cumulative divergence; Heavy-tailed data; Index direction; Single index model; Sufficient dimension reduction (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:202:y:2025:i:c:s0167947324001361

DOI: 10.1016/j.csda.2024.108052

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