  In health-pollution cohort studies, accurate predictions of pollutant
concentrations at new locations are needed, since the locations of fixed
monitoring sites and study participants are often spatially misaligned. For
multi-pollution data, principal component analysis (PCA) is often incorporated
to obtain low-rank (LR) structure of the data prior to spatial prediction.
Recently developed predictive PCA modifies the traditional algorithm to improve
the overall predictive performance by leveraging both LR and spatial structures
within the data. However, predictive PCA requires complete data or an initial
imputation step. Nonparametric imputation techniques without accounting for
spatial information may distort the underlying structure of the data, and thus
further reduce the predictive performance. We propose a convex optimization
problem inspired by the LR matrix completion framework and develop a proximal
algorithm to solve it. Missing data are imputed and handled concurrently within
the algorithm, which eliminates the necessity of a separate imputation step. We
show that our algorithm has low computational burden and leads to reliable
predictive performance as the severity of missing data increases.
