Block Empirical Likelihood Inference for Longitudinal Generalized Partially Linear Single-Index Models
Abstract
Generalized partially linear single-index models (GPLSIMs) provide a flexible and interpretable semiparametric framework for longitudinal outcomes by combining a low-dimensional parametric component with a nonparametric index component. For repeated measurements, valid inference is challenging because within-subject correlation induces nuisance parameters and variance estimation can be unstable in semiparametric settings. We propose a profile estimating-equation approach based on spline approximation of the unknown link function and construct a subject-level block empirical likelihood (BEL) for joint inference on the parametric coefficients and the single-index direction. The resulting BEL ratio statistic enjoys a Wilks-type chi-square limit, yielding likelihood-free confidence regions without explicit sandwich variance estimation. We also discuss practical implementation, including constrained optimization for the index parameter, working-correlation choices, and bootstrap-based confidence bands for the nonparametric component. Simulation studies and an application to the epilepsy longitudinal study illustrate the finite-sample performance.
Cite
@article{arxiv.2602.14981,
title = {Block Empirical Likelihood Inference for Longitudinal Generalized Partially Linear Single-Index Models},
author = {Tianni Zhang and Yuyao Wang and Yu Lu and Mengfei Ran},
journal= {arXiv preprint arXiv:2602.14981},
year = {2026}
}