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Score estimation in the monotone single‐index model

Author

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  • Fadoua Balabdaoui
  • Piet Groeneboom
  • Kim Hendrickx

Abstract

We consider estimation in the single‐index model where the link function is monotone. For this model, a profile least‐squares estimator has been proposed to estimate the unknown link function and index. Although it is natural to propose this procedure, it is still unknown whether it produces index estimates that converge at the parametric rate. We show that this holds if we solve a score equation corresponding to this least‐squares problem. Using a Lagrangian formulation, we show how one can solve this score equation without any reparametrization. This makes it easy to solve the score equations in high dimensions. We also compare our method with the effective dimension reduction and the penalized least‐squares estimator methods, both available on CRAN as R packages, and compare with link‐free methods, where the covariates are elliptically symmetric.

Suggested Citation

  • Fadoua Balabdaoui & Piet Groeneboom & Kim Hendrickx, 2019. "Score estimation in the monotone single‐index model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 46(2), pages 517-544, June.
    • Handle: RePEc:bla:scjsta:v:46:y:2019:i:2:p:517-544
    DOI: 10.1111/sjos.12361
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    Citations

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    Cited by:

    1. Yoichi Arai & Taisuke Otsu & Mengshan Xu, 2022. "GLS under Monotone Heteroskedasticity," Papers 2210.13843, arXiv.org, revised Jan 2024.
    2. Yoici Arai & Taisuke Otsu & Mengshan Xu, 2022. "GLS under monotone heteroskedasticity," STICERD - Econometrics Paper Series 625, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    3. Taisuke Otsu & Mengshan Xu, 2022. "Isotonic propensity score matching," STICERD - Econometrics Paper Series 623, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    4. Fadoua Balabdaoui & Cécile Durot & Christopher Fragneau, 2021. "On the population least‐squares criterion in the monotone single index model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(4), pages 408-436, November.
    5. Xu, Mengshan & Otsu, Taisuke, 2020. "Score estimation of monotone partially linear index model," LSE Research Online Documents on Economics 106698, London School of Economics and Political Science, LSE Library.
    6. Otsu, Taisuke & Takahata, Keisuke & Xu, Mengshan, 2023. "Empirical likelihood inference for monotone index model," LSE Research Online Documents on Economics 118123, London School of Economics and Political Science, LSE Library.
    7. Mengshan Xu & Taisuke Otsu, 2022. "Isotonic propensity score matching," Papers 2207.08868, arXiv.org, revised Aug 2024.

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