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<p>A flexible functional additive model is proposed to predict a scalar response by incorporating the nonparametric effects of high-dimensional functional predictors. Specifically, we project the cross-correlated high-dimensional functional predictors onto uncorrelated principal component scores using multivariate functional principal component analysis (MFPCA). The standardized MFPCA scores are then modeled additively to capture the nonparametric effects. The primary challenge in model estimation lies in accurately estimating the standardized MFPCA scores. To ensure consistent estimation in high-dimensional settings, a sparse structure is first imposed on the covariance function. We then apply adaptive thresholding to shrink the entries of the sample covariance function, aiming to obtain consistent estimators of both the covariance function and the standardized MFPCA scores. Given the infinite-dimensional nature of functional data, we allow the number of additive components to grow slowly with the sample size. Moreover, we combine B-splines and adaptive group least absolute shrinkage and selection operator (LASSO) to simultaneously select and estimate the relevant components. Under some mild conditions, the convergence rate of the standardized MFPCA scores is established, and the consistency of component selection and estimation within the additive model is demonstrated. Finally, the empirical performance of the proposed method is validated through simulations and an application to a fluorescence spectroscopy dataset.</p>

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Estimation in functional additive models for high-dimensional functional data

  • 期刊论文

  • 发表日期：

    2026年2月25日

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  • Yilun Wang,
  • Yuan Xue,
  • Yuping Hu,
  • Gaorong Li

摘要

A flexible functional additive model is proposed to predict a scalar response by incorporating the nonparametric effects of high-dimensional functional predictors. Specifically, we project the cross-correlated high-dimensional functional predictors onto uncorrelated principal component scores using multivariate functional principal component analysis (MFPCA). The standardized MFPCA scores are then modeled additively to capture the nonparametric effects. The primary challenge in model estimation lies in accurately estimating the standardized MFPCA scores. To ensure consistent estimation in high-dimensional settings, a sparse structure is first imposed on the covariance function. We then apply adaptive thresholding to shrink the entries of the sample covariance function, aiming to obtain consistent estimators of both the covariance function and the standardized MFPCA scores. Given the infinite-dimensional nature of functional data, we allow the number of additive components to grow slowly with the sample size. Moreover, we combine B-splines and adaptive group least absolute shrinkage and selection operator (LASSO) to simultaneously select and estimate the relevant components. Under some mild conditions, the convergence rate of the standardized MFPCA scores is established, and the consistency of component selection and estimation within the additive model is demonstrated. Finally, the empirical performance of the proposed method is validated through simulations and an application to a fluorescence spectroscopy dataset.