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<p>We investigate non-parametric inference for the population mean function of a stochastic process when each trajectory is observed at only a few irregular time points. Working with a smoothing spline estimator in a reproducing kernel Hilbert space, we develop a new maximal inequality for the underlying empirical process and derive a Bahadur representation that yields pointwise asymptotic normality. We construct a confidence intervals and a penalised likelihood-ratio test for the mean function at a fixed time point.</p>

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On asymptotic properties of mean function estimator for sparse noise-contaminated data

  • 期刊论文

  • 发表日期：

    2025年9月17日

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  • Mustafa Abduljabbar Dawood,
  • Behdad Mostafaiy

摘要

We investigate non-parametric inference for the population mean function of a stochastic process when each trajectory is observed at only a few irregular time points. Working with a smoothing spline estimator in a reproducing kernel Hilbert space, we develop a new maximal inequality for the underlying empirical process and derive a Bahadur representation that yields pointwise asymptotic normality. We construct a confidence intervals and a penalised likelihood-ratio test for the mean function at a fixed time point.