Empirical likelihood for single-index varying-coefficient models

TL;DR

This paper introduces empirical likelihood-based inference methods for single-index varying-coefficient models, providing efficient estimators and confidence regions for both parametric and nonparametric components.

Contribution

It develops a novel empirical likelihood approach for inference in single-index varying-coefficient models, achieving asymptotic efficiency and optimal convergence rates.

Findings

Estimator for parametric component is asymptotically efficient.

Estimator for nonparametric component has optimal convergence rate.

Simulation study confirms good finite sample performance.

Abstract

In this paper, we develop statistical inference techniques for the unknown coefficient functions and single-index parameters in single-index varying-coefficient models. We first estimate the nonparametric component via the local linear fitting, then construct an estimated empirical likelihood ratio function and hence obtain a maximum empirical likelihood estimator for the parametric component. Our estimator for parametric component is asymptotically efficient, and the estimator of nonparametric component has an optimal convergence rate. Our results provide ways to construct the confidence region for the involved unknown parameter. We also develop an adjusted empirical likelihood ratio for constructing the confidence regions of parameters of interest. A simulation study is conducted to evaluate the finite sample behaviors of the proposed methods.