# Entrywise Inference for Missing Panel Data: A Simple and Instance-Optimal Approach

arXiv: https://arxiv.org/abs/2401.13665 · HTML: https://mlsanity.com/paper/2401.13665/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jan 2024.

## Built on by (most cited first, 7 of 7)

- [When can weak latent factors be statistically inferred?](https://mlsanity.com/paper/2407.03616/) (2024)
- [Learning Counterfactual Distributions via Kernel Nearest Neighbors](https://mlsanity.com/paper/2410.13381/) (2024)
- [Covariate-Adjusted Deep Causal Learning for Heterogeneous Panel Data Models](https://mlsanity.com/paper/2505.20536/) (2025)
- [Cluster Quilting: Spectral Clustering for Patchwork Learning](https://mlsanity.com/paper/2406.13833/) (2024)
- [Robust Matrix Estimation with Side Information](https://mlsanity.com/paper/2603.24833/) (2026)
- [Geometric bias in eigenspace perturbation under random heterogeneous noise](https://mlsanity.com/paper/2606.11263/) (2026)
- [Synthetic Nearest Neighbors: Extending Synthetic Controls for Matrix Completion with Missing Not at Random Data](https://mlsanity.com/paper/2609.13586/) (2026)

## Abstract (arXiv)

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 Cram'er-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.