Empirical Likelihood Confidence Intervals for Nonparametric Functional Data Analysis

TL;DR

This paper develops empirical likelihood-based confidence intervals for nonparametric functional data analysis, demonstrating Wilks's phenomenon and bias correction, with improved performance over traditional asymptotic methods.

Contribution

It introduces a bias-corrected empirical likelihood method for functional data, avoiding undersmoothing and bias estimation, and extends results to partially linear models.

Findings

Empirical likelihood exhibits Wilks's phenomenon in this context.

Bias correction improves coverage accuracy.

Outperforms asymptotic normality-based methods in simulations.

Abstract

We consider the problem of constructing confidence intervals for nonparametric functional data analysis using empirical likelihood. In this doubly infinite-dimensional context, we demonstrate the Wilks's phenomenon and propose a bias-corrected construction that requires neither undersmoothing nor direct bias estimation. We also extend our results to partially linear regression involving functional data. Our numerical results demonstrated the improved performance of empirical likelihood over approximation based on asymptotic normality.