monomvn: Estimation for multivariate normal and Student-t data with monotone missingness. Estimation of multivariate normal and student-t data of arbitrary dimension where the pattern of missing data is monotone. Through the use of parsimonious/shrinkage regressions (plsr, pcr, lasso, ridge, etc.), where standard regressions fail, the package can handle a nearly arbitrary amount of missing data. The current version supports maximum likelihood inference and a full Bayesian approach employing scale-mixtures for Gibbs sampling. Monotone data augmentation extends this Bayesian approach to arbitrary missingness patterns. A fully functional standalone interface to the Bayesian lasso (from Park & Casella), Normal-Gamma (from Griffin & Brown), Horseshoe (from Carvalho, Polson, & Scott), and ridge regression with model selection via Reversible Jump, and student-t errors (from Geweke) is also provided