Noisy matrix completion for longitudinal data with subject- and time-specific covariates

In this article, we consider the imputation of missing responses in a longitudinal dataset via matrix completion. We propose a fixed-effect, longitudinal, low-rank model that incorporates both subject-specific and time-specific covariates. To solve the optimization problem, a two-step optimization algorithm is proposed, which provides good statistical properties for the estimation of the fixed effects and the low-rank term. In a theoretical investigation, the non-asymptotic error bounds on the fixed effects and low-rank term are presented. We illustrate the finite-sample performance of the proposed algorithm via simulation studies, and apply our method to a power plant SO${}_2$ emissions dataset in which the monthly recorded amounts of emissions data on monitors are subject to missingness.