Prediction in functional regression with discretely observed and noisy covariates

TL;DR

This paper proposes a factor model-based approach for prediction in functional regression with discretely observed, noisy data, demonstrating its efficiency and effectiveness through theoretical analysis and empirical validation.

Contribution

It introduces a factor model method for functional regression with noisy, discretely observed data, showing its consistency and practical advantages over scalar-on-function regression.

Findings

Factor model approach is numerically efficient.

Method performs well in simulations and real data.

Limited gain from embedding into scalar-on-function regression.

Abstract

In practice functional data are sampled on a discrete set of observation points and often susceptible to noise. We consider in this paper the setting where such data are used as explanatory variables in a regression problem. If the primary goal is prediction, we show that the gain by embedding the problem into a scalar-on-function regression is limited. Instead we impose a factor model on the predictors and suggest regressing the response on an appropriate number of factor scores. This approach is shown to be consistent under mild technical assumptions, numerically efficient and gives good practical performance in both simulations as well as real data settings.