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Connections between two classes of estimators for single‐index models

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  • Weichao Yang
  • Xu Guo
  • Niwen Zhou
  • Changliang Zou

Abstract

Single‐index model is a very popular and powerful semiparametric model. As an improvement of the maximum rank correlation estimator, Shen et al. proposed the linearized maximum rank correlation estimator. We show that this estimator has some interesting connections with the distribution‐transformed least‐squares estimator for single‐index models. We also propose a rescaled distribution‐transformed least‐squares estimator, which is mathematically equivalent to the linearized maximum rank correlation estimator when the distribution of the response is absolutely continuous. Despite some nontrivial connections, the two estimation procedures are different in terms of motivations, interpretations, and applications. We discuss some of the differences between the two estimation procedures.

Suggested Citation

  • Weichao Yang & Xu Guo & Niwen Zhou & Changliang Zou, 2024. "Connections between two classes of estimators for single‐index models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 78(3), pages 485-490, August.
    • Handle: RePEc:bla:stanee:v:78:y:2024:i:3:p:485-490
    DOI: 10.1111/stan.12329
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    References listed on IDEAS

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    1. Zhu, Li-Ping & Zhu, Li-Xing, 2009. "Nonconcave penalized inverse regression in single-index models with high dimensional predictors," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 862-875, May.
    2. Han, Aaron K., 1987. "Non-parametric analysis of a generalized regression model : The maximum rank correlation estimator," Journal of Econometrics, Elsevier, vol. 35(2-3), pages 303-316, July.
    3. Guohao Shen & Kani Chen & Jian Huang & Yuanyuan Lin, 2023. "Linearized maximum rank correlation estimation," Biometrika, Biometrika Trust, vol. 110(1), pages 187-203.
    4. Feng, Zhenghui & Wang, Tao & Zhu, Lixing, 2014. "Transformation-based estimation," Computational Statistics & Data Analysis, Elsevier, vol. 78(C), pages 186-205.
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