What question did this study set out to answer?

The research aims to develop a k-nearest neighbor regression method using distance-exponent weighting for scalar-on-function data.

Adaptive functional kernel kNN regression via distance-exponent weighting

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Randomized trial demonstrates pointwise consistency in kernel kNN regression, suggesting improved accuracy in function-based predictions.

The research aims to develop a k-nearest neighbor regression method using distance-exponent weighting for scalar-on-function data.
Introduced a distance-exponent weighting scheme within the kNN neighborhood.
Established consistency and bias-variance bounds under standard assumptions and conditions.
Utilized simulation experiments and application to spectrometric data for performance illustration.
Achieved usual convergence rates under local Hölder smoothness with explicit bias expansion.
Showed that increasing the exponent can reduce bias constant without affecting variance order.
Cross-validation recommended for practical selection of tuning parameters.

Bouabsa et al. (2026) studied this question.

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