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Robust direction estimation in single-index models via cumulative divergence

Author

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  • He, Shuaida
  • Zhang, Jiarui
  • Chen, Xin

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.

Suggested Citation

  • He, Shuaida & Zhang, Jiarui & Chen, Xin, 2025. "Robust direction estimation in single-index models via cumulative divergence," Computational Statistics & Data Analysis, Elsevier, vol. 202(C).
    • Handle: RePEc:eee:csdana:v:202:y:2025:i:c:s0167947324001361
    DOI: 10.1016/j.csda.2024.108052
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