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<p>The objective of this article is to estimate, non-parametrically the conditional distribution function of a scalar response variable taking values in separable Hilbert space. We suppose that the response variable is left truncated data. We introduce the kernel type estimators for the conditional distribution function. Then, we establish the pointwise almost complete convergence and the uniform almost complete convergence (with rate) of the kernels estimators based on the single-index structure. Finally, we give the asymptotic properties of the conditional distribution function.</p>

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Asymptotic Properties of a Conditional Distribution Estimator in Single Functional Index Model with Randomly Truncated Data

  • 期刊论文

  • 发表日期：

    2026年7月30日

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  • Sanaà Dounya Mekki,
  • Abbes Rabhi,
  • Mohamed Mehdi Hamri,
  • Abdassamad Dib

摘要

The objective of this article is to estimate, non-parametrically the conditional distribution function of a scalar response variable taking values in separable Hilbert space. We suppose that the response variable is left truncated data. We introduce the kernel type estimators for the conditional distribution function. Then, we establish the pointwise almost complete convergence and the uniform almost complete convergence (with rate) of the kernels estimators based on the single-index structure. Finally, we give the asymptotic properties of the conditional distribution function.