Convergence analysis of function-on-function polynomial regression model
Abstract
In this paper, we study the convergence behavior of the regularization-based algorithm for solving the polynomial regression model when both input data and responses are from infinite-dimensional Hilbert spaces. We derive convergence rates for estimation and prediction error by employing general (spectral) regularization under a general smoothness condition without imposing any additional conditions on the index function. We also establish lower bounds for any learning algorithm to explain the optimality of our convergence rates.
Fields of Study & Subjects
Statistical Methods and Inference
Stochastic Gradient Optimization Techniques
Sparse and Compressive Sensing Techniques
Publication details
- Journal / source
- Analysis and Applications
- Publisher
- World Scientific Pub Co Pte Ltd
- Pages
- 1–26
- Publication date
- 7 August 2026
- Language
- EN