2024/01/24 by Yan, Yuling, Wainwright, Martin J. · 1 citation
#Econometrics (econ.EM) #FOS: Computer and information sciences #FOS: Economics and business #FOS: Mathematics #Machine Learning (stat.ML) #Methodology (stat.ME) #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.2401.13665
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.