# Block Empirical Likelihood Inference for Longitudinal Generalized Partially Linear Single-Index Models

arXiv: https://arxiv.org/abs/2602.14981 · HTML: https://mlsanity.com/paper/2602.14981/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 34 references that are in the map.
- First posted on arXiv 16 Feb 2026.

## Builds on (most cited first, 1 of 1)

- [Empirical likelihood inference for longitudinal data with covariate measurement errors: An application to the LEAN study](https://mlsanity.com/paper/2110.02449/) (2021)

## Abstract (arXiv)

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.