Hypothesis Testing for Penalized Estimating Equations with Cross-Fitted Covariance Calibration
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866918430549999616 |
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| author | Zhou, Jing Zhang, Zhe |
| author_facet | Zhou, Jing Zhang, Zhe |
| contents | We study hypothesis testing for penalized estimators in settings where the full marginal distribution of a multivariate response is difficult to specify, such as longitudinal data with correlated measurements or high-dimensional heteroscedastic regression. Assuming that the conditional mean model is correctly specified, we establish that the penalized estimating equations admit a $\sqrt{n}$-consistent solution, even when the working covariance structure is misspecified. Our inferential target is a low-dimensional subvector of parameters associated with the mean model. We show that the resulting test statistic converges to a $χ^2$ distribution, and that its asymptotic power depends on the nuisance covariance function. To mitigate this dependence, we propose estimating the covariance function via cross-fitting, which provides a calibrated and robust procedure for inference. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_05055 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hypothesis Testing for Penalized Estimating Equations with Cross-Fitted Covariance Calibration Zhou, Jing Zhang, Zhe Methodology Statistics Theory We study hypothesis testing for penalized estimators in settings where the full marginal distribution of a multivariate response is difficult to specify, such as longitudinal data with correlated measurements or high-dimensional heteroscedastic regression. Assuming that the conditional mean model is correctly specified, we establish that the penalized estimating equations admit a $\sqrt{n}$-consistent solution, even when the working covariance structure is misspecified. Our inferential target is a low-dimensional subvector of parameters associated with the mean model. We show that the resulting test statistic converges to a $χ^2$ distribution, and that its asymptotic power depends on the nuisance covariance function. To mitigate this dependence, we propose estimating the covariance function via cross-fitting, which provides a calibrated and robust procedure for inference. |
| title | Hypothesis Testing for Penalized Estimating Equations with Cross-Fitted Covariance Calibration |
| topic | Methodology Statistics Theory |
| url | https://arxiv.org/abs/2604.05055 |