Cluster-Robust Inference for Quadratic Forms
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866917277551558656 |
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| author | Kolesár, Michal Min, Pengjin Wang, Wenjie Zhang, Yichong |
| author_facet | Kolesár, Michal Min, Pengjin Wang, Wenjie Zhang, Yichong |
| contents | This paper studies inference for quadratic forms of linear regression coefficients with clustered data and many covariates. Our framework covers three important special cases: instrumental variables regression with many instruments and controls, inference on variance components, and testing multiple restrictions in a linear regression. Na\"ıve plug-in estimators are known to be biased. We study a leave-one-cluster-out estimator that is unbiased, and provide sufficient conditions for its asymptotic normality. For inference, we establish the consistency of a leave-three-cluster-out variance estimator under primitive conditions. In addition, we develop a novel leave-two-cluster-out variance estimator that is computationally simpler and guaranteed to be conservative under weaker conditions. Our analysis allows cluster sizes to diverge with the sample size, accommodates strong within-cluster dependence, and permits the dimension of the covariates to diverge with the sample size, potentially at the same rate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_13537 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Cluster-Robust Inference for Quadratic Forms Kolesár, Michal Min, Pengjin Wang, Wenjie Zhang, Yichong Econometrics This paper studies inference for quadratic forms of linear regression coefficients with clustered data and many covariates. Our framework covers three important special cases: instrumental variables regression with many instruments and controls, inference on variance components, and testing multiple restrictions in a linear regression. Na\"ıve plug-in estimators are known to be biased. We study a leave-one-cluster-out estimator that is unbiased, and provide sufficient conditions for its asymptotic normality. For inference, we establish the consistency of a leave-three-cluster-out variance estimator under primitive conditions. In addition, we develop a novel leave-two-cluster-out variance estimator that is computationally simpler and guaranteed to be conservative under weaker conditions. Our analysis allows cluster sizes to diverge with the sample size, accommodates strong within-cluster dependence, and permits the dimension of the covariates to diverge with the sample size, potentially at the same rate. |
| title | Cluster-Robust Inference for Quadratic Forms |
| topic | Econometrics |
| url | https://arxiv.org/abs/2602.13537 |