Block Empirical Likelihood Inference for Longitudinal Generalized Partially Linear Single-Index Models
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914336040026112 |
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| author | Zhang, Tianni Wang, Yuyao Lu, Yu Ran, Mengfei |
| author_facet | Zhang, Tianni Wang, Yuyao Lu, Yu Ran, Mengfei |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14981 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Block Empirical Likelihood Inference for Longitudinal Generalized Partially Linear Single-Index Models Zhang, Tianni Wang, Yuyao Lu, Yu Ran, Mengfei Methodology Statistics Theory Computation Machine Learning 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. |
| title | Block Empirical Likelihood Inference for Longitudinal Generalized Partially Linear Single-Index Models |
| topic | Methodology Statistics Theory Computation Machine Learning |
| url | https://arxiv.org/abs/2602.14981 |