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

Haihan Xie and Linglong Kong

Journal of Multivariate Analysis, 2023, vol. 198, issue C

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.

Keywords: Copula model; Function-on-scalar regression; Image analysis; Optimal rate of convergence; Statistical inference (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.jmva.2023.105226

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