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

TL;DR

This paper introduces a simple, efficient, and instance-optimal method for entrywise inference in missing panel data, providing accurate estimation and confidence intervals with strong theoretical guarantees.

Contribution

It presents a novel, computationally efficient approach for entrywise inference in missing panel data, with proven instance-optimal confidence intervals matching lower bounds.

Findings

Method achieves non-asymptotic error bounds.

Confidence intervals have guaranteed coverage.

Numerical examples demonstrate sharpness of theoretical results.

Abstract

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\'{e}r-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.