Entrywise Inference for Missing Panel Data: A Simple and Instance-Optimal Approach
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913411215917056 |
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| author | Yan, Yuling Wainwright, Martin J. |
| author_facet | Yan, Yuling Wainwright, Martin J. |
| contents | Longitudinal or panel data can be represented as a matrix with rows indexed by units and columns indexed by time. We consider inferential questions associated with the missing data version of panel data induced by staggered adoption. We propose a computationally efficient procedure for estimation, involving only simple matrix algebra and singular value decomposition, and prove non-asymptotic and high-probability bounds on its error in estimating each missing entry. By controlling proximity to a suitably scaled Gaussian variable, we develop and analyze a data-driven procedure for constructing entrywise confidence intervals with pre-specified coverage. Despite its simplicity, our procedure turns out to be instance-optimal: we prove that the width of our confidence intervals match a non-asymptotic instance-wise lower bound derived via a Bayesian Cramér-Rao argument. We illustrate the sharpness of our theoretical characterization on a variety of numerical examples. Our analysis is based on a general inferential toolbox for SVD-based algorithm applied to the matrix denoising model, which might be of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_13665 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Entrywise Inference for Missing Panel Data: A Simple and Instance-Optimal Approach Yan, Yuling Wainwright, Martin J. Statistics Theory Econometrics Methodology Machine Learning Longitudinal or panel data can be represented as a matrix with rows indexed by units and columns indexed by time. We consider inferential questions associated with the missing data version of panel data induced by staggered adoption. We propose a computationally efficient procedure for estimation, involving only simple matrix algebra and singular value decomposition, and prove non-asymptotic and high-probability bounds on its error in estimating each missing entry. By controlling proximity to a suitably scaled Gaussian variable, we develop and analyze a data-driven procedure for constructing entrywise confidence intervals with pre-specified coverage. Despite its simplicity, our procedure turns out to be instance-optimal: we prove that the width of our confidence intervals match a non-asymptotic instance-wise lower bound derived via a Bayesian Cramér-Rao argument. We illustrate the sharpness of our theoretical characterization on a variety of numerical examples. Our analysis is based on a general inferential toolbox for SVD-based algorithm applied to the matrix denoising model, which might be of independent interest. |
| title | Entrywise Inference for Missing Panel Data: A Simple and Instance-Optimal Approach |
| topic | Statistics Theory Econometrics Methodology Machine Learning |
| url | https://arxiv.org/abs/2401.13665 |