What question did this study set out to answer?

This research aims to understand how well a polynomial regression model performs in infinite-dimensional spaces using regularization techniques.

August 10, 2026Analysis and ApplicationsOpen Access

Convergence analysis of function-on-function polynomial regression model

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The analysis reveals convergence rates for estimation and prediction error in infinite-dimensional spaces, suggesting optimal learning algorithms.

This research aims to understand how well a polynomial regression model performs in infinite-dimensional spaces using regularization techniques.
Investigated convergence behavior of a polynomial regression model in infinite-dimensional Hilbert spaces
Derived convergence rates for estimation and prediction error under general smoothness conditions
Established lower bounds for learning algorithms to demonstrate the optimality of derived convergence rates.
Convergence rates were successfully derived for both estimation and prediction errors.
Lower bounds established provide insight into the optimality of the convergence rates achieved.
The algorithm exhibits effective convergence behavior without additional conditions on the index function.

Gupta et al. (2026) studied this question.

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The analysis reveals convergence rates for estimation and prediction error in infinite-dimensional spaces, suggesting optimal learning algorithms.