What question did this study set out to answer?

To introduce a robust nonparametric regression methodology for functional predictors capable of handling nonlinear relationships, heavy-tailed score distributions, and response contamination.

August 15, 2026MathematicsOpen Access

Robust Functional Regression via FPCA, Copula-Scale Design, and Multivariate Bernstein Smoothing

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Authors

WBWahiba BouabsaPrincess Nourah bint Abdulrahman University FAFatimah AlshahraniPrincess Nourah bint Abdulrahman University

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Implication

Methodological analysis demonstrates a robust nonparametric functional regression framework, highlighting resilience against heavy-tailed noise and extreme response contamination.

Key Points

To introduce a robust nonparametric regression methodology for functional predictors capable of handling nonlinear relationships, heavy-tailed score distributions, and response contamination.
Reduced infinite-dimensional functional predictors into low-dimensional representations using functional principal component analysis (FPCA) and transformed retained scores to a unit cube via marginal copula normalization.
Estimated conditional M-functionals by combining bounded-score M-estimation with multivariate Bernstein smoothing over local estimating equations.
Evaluated theoretical asymptotic consistency and tested finite-sample predictive performance through simulations with Student-t errors, heavy-tailed scores, and response contamination.
Established pointwise and uniform consistency, explicit convergence rates, and asymptotic normality, identifying an explicit Bernstein concentration factor within the limiting variance.
Demonstrated strong finite-sample predictive accuracy and robustness against contamination and heavy-tailed noise across simulations, particularly under absolute-error performance metrics.

Cite This Study

Bouabsa et al. (2026) studied this question.

synapsesocial.com/papers/6a8019db75c2e31742c8621e https://doi.org/10.3390/math14162935

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Implication

Methodological analysis demonstrates a robust nonparametric functional regression framework, highlighting resilience against heavy-tailed noise and extreme response contamination.

Robust Functional Regression via FPCA, Copula-Scale Design, and Multivariate Bernstein Smoothing

Discussion

Member takes

Implication

Key Points

Cite This Study

Robust Functional Regression via FPCA, Copula-Scale Design, and Multivariate Bernstein Smoothing

Discussion

Member takes

Implication

Key Points

Cite This Study

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