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<p>We propose a new nonparametric conditional mean independence test for a scalar response and a functional covariate. The test statistics are built from continuous functionals over a residual marked empirical process indexed by a randomly projected functional covariate, which is less sensitive to tuning parameters and circumvents the curse of dimensionality. The asymptotic properties of the proposed test statistics under the null and the fixed alternative are established. We also show that our proposed test is able to detect a broad class of local alternatives converging to the null at the parametric rate. Due to the non-pivotal limiting null distribution, we use an easy-to-implement multiplier bootstrap procedure to estimate the critical values. Monte Carlo simulation studies demonstrate that our test outperforms other tests available in the literature due to its higher power and computational efficiency. The proposed test is further illustrated by analyzing the Tecator data set.</p>

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Testing mean independence with functional covariate

  • 期刊论文

  • 发表日期：

    2025年8月14日

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  • Yongzhen Feng,
  • Jie Li,
  • Haokun Lu,
  • Xiaojun Song

摘要

We propose a new nonparametric conditional mean independence test for a scalar response and a functional covariate. The test statistics are built from continuous functionals over a residual marked empirical process indexed by a randomly projected functional covariate, which is less sensitive to tuning parameters and circumvents the curse of dimensionality. The asymptotic properties of the proposed test statistics under the null and the fixed alternative are established. We also show that our proposed test is able to detect a broad class of local alternatives converging to the null at the parametric rate. Due to the non-pivotal limiting null distribution, we use an easy-to-implement multiplier bootstrap procedure to estimate the critical values. Monte Carlo simulation studies demonstrate that our test outperforms other tests available in the literature due to its higher power and computational efficiency. The proposed test is further illustrated by analyzing the Tecator data set.