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

• URL: http://arxiv.org/abs/2602.14981v2
• Date: Wed, 18 Feb 2026 10:47:59 GMT
• Title: Block Empirical Likelihood Inference for Longitudinal Generalized Partially Linear Single-Index Models
• Authors: Tianni Zhang, Yuyao Wang, Yu Lu, Mengfei Ran,
• Abstract summary: Generalized partially linear single-index models (GPLSIMs) provide a flexible and interpretable semiparametric framework for longitudinal outcomes.<n>For repeated measurements, valid inference is challenging because within-subject correlation induces nuisance parameters and variance estimation can be unstable in semiparametric settings.<n>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.
• Score: 9.83545269451662
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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