Large Deviations Theorems in Nonparametric Regression on Functional Data

TL;DR

This paper establishes large deviations principles for the Nadaraya-Watson estimator in nonparametric regression involving functional data, providing theoretical insights into the estimator's probabilistic behavior.

Contribution

It introduces large deviations theorems for the Nadaraya-Watson estimator in the context of functional data regression, extending existing theory.

Findings

Proves pointwise large deviations principles.

Establishes uniform large deviations results.

Provides explicit rate functions.

Abstract

In this paper we prove large deviations principles for the Nadaraya-Watson estimator of the regression of a real-valued variable with a functional covariate. Under suitable conditions, we show pointwise and uniform large deviations theorems with good rate functions.