Estimation for Single-Index mixed models with Longitudinal data

TL;DR

This paper introduces new estimation methods for single-index mixed models with longitudinal data, achieving optimal convergence rates and asymptotic normality, enabling reliable inference and hypothesis testing.

Contribution

It proposes a novel set of estimating equations and uses local linear smoothing for the link function, with proven asymptotic properties and practical validation.

Findings

Estimators of the link function achieve optimal convergence rates.

Variance component estimators have root-n consistency.

Simulation and real data analysis validate the methods.

Abstract

In this paper, we consider a single-index mixed model with longitudinal data. A new set of estimating equations is proposed to estimate the single-index coefficient. The link function is estimated by using the local linear smoothing. Asymptotic normality is established for the proposed estimators. Also, the estimator of the link function achieves optimal convergence rates; and the estimators of variance components have root-$n$ consistency. These results facilitate the construction of confidence regions/intervals and hypothesis testing for the parameters of interest. Some simulations and an application to real data are included.