# Functional continuum regression

## TL;DR

This paper introduces functional continuum regression, a new method that improves prediction accuracy in functional data analysis by encompassing and extending existing techniques like PCR and PLS.

## Contribution

The paper develops a novel functional continuum regression framework that unifies and generalizes PCR and PLS, with proven consistency and improved prediction performance.

## Key findings

- Functional CR outperforms PCR and PLS in simulations.
- Functional CR provides consistent estimators.
- Numerical case studies demonstrate improved accuracy.

## Abstract

Functional principal component regression (PCR) can fail to provide good prediction if the response is highly correlated with some excluded functional principal component(s). This situation is common since the construction of functional principal components never involves the response. Aiming at this shortcoming, we develop functional continuum regression (CR). The framework of functional CR includes, as special cases, both functional PCR and functional partial least squares (PLS). Functional CR is expected to own a better accuracy than functional PCR and functional PLS both in estimation and prediction; evidence for this is provided through simulation and numerical case studies. Also, we demonstrate the consistency of estimators given by functional CR.