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Gaussian copula function-on-scalar regression in reproducing kernel Hilbert space

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  • Xie, Haihan
  • Kong, Linglong

Abstract

To relax the linear assumption in function-on-scalar regression, we borrow the strength of copula and propose a novel Gaussian copula function-on-scalar regression. Our model is more flexible to characterize the dynamic relationship between functional response and scalar predictors. Estimation, prediction, and inference are fully investigated. We develop a closed form for the estimator of coefficient functions in a reproducing kernel Hilbert space without the knowledge of marginal transformations. Valid, distribution-free, finite-sample prediction bands are constructed via conformal prediction. Theoretically, we establish the optimal convergence rate on the estimation of coefficient functions and show that our proposed estimator is rate-optimal under fixed and random designs. The finite-sample performance is investigated through simulations and illustrated in real data analysis.

Suggested Citation

  • Xie, Haihan & Kong, Linglong, 2023. "Gaussian copula function-on-scalar regression in reproducing kernel Hilbert space," Journal of Multivariate Analysis, Elsevier, vol. 198(C).
    • Handle: RePEc:eee:jmvana:v:198:y:2023:i:c:s0047259x23000726
    DOI: 10.1016/j.jmva.2023.105226
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    References listed on IDEAS

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