Nonparametric regression based on discretely sampled curves

TL;DR

This paper investigates how the consistency of nonparametric regression estimators from discretely sampled curves relates to that from full trajectories, providing asymptotic results for common functional data analysis methods.

Contribution

It establishes conditions linking the consistency of estimators from discrete samples to those from complete trajectories, applicable to various regularization techniques.

Findings

Derived asymptotic results for smoothing methods.

Linked discrete sample estimator consistency to full trajectory estimators.

Applicable to basis representation techniques.

Abstract

In the context of nonparametric regression, we study conditions under which the consistency (and rates of convergence) of estimators built from discretely sampled curves can be derived from the consistency of estimators based on the unobserved whole trajectories. As a consequence, we derive asymptotic results for most of the regularization techniques used in functional data analysis, including smoothing and basis representation.