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<p>In this work, we construct and study a family of robust nonparametric estimators for a regression function based on kernel methods. The data are functional, independent and identically distributed, and are linked to a single-index model. Under general conditions, we establish the pointwise and uniform almost complete convergence, as well as the asymptotic normality of the estimator. We explicitly derive the asymptotic variance and, as a result, provide confidence bands for the theoretical parameter. A simulation study is conducted to illustrate the proposed methodology.</p>

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On the Robust Nonparametric Regression Estimate in the Single Functional Index Model

  • 期刊论文

  • 发表日期：

    2025年5月24日

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  • Billal Bentata,
  • Said Attaoui,
  • Elias Ould-Saïd

摘要

In this work, we construct and study a family of robust nonparametric estimators for a regression function based on kernel methods. The data are functional, independent and identically distributed, and are linked to a single-index model. Under general conditions, we establish the pointwise and uniform almost complete convergence, as well as the asymptotic normality of the estimator. We explicitly derive the asymptotic variance and, as a result, provide confidence bands for the theoretical parameter. A simulation study is conducted to illustrate the proposed methodology.