Although the random sampling distribution must be considered when making inferences from sample survey data, this distribution is rarely sufficient because of many features of applied sampling. These features include nonresponse, response bias, and data relationships that make applied sampling a multivariate discipline where univariate methods generally fail to produce optimal inferences. In spite of this, sample survey inference has remained largely univariate with an encyclopedia of corrective techniques to handle these negative features of sample data. This paper discusses theory and applications of multivariate methods for estimating finite population mean vectors assuming data deficiencies like nonresponse (both item and total, ignorable and otherwise) and response bias, but exploiting data dependencies modeled by the covariance matrix of survey variables (both design and target variables). These data dependencies are used to minimize mean square error in the presence of the data deficiencies. The estimator so derived, automatically handles many missing data problems that practitioners face by fully exploiting known data dependencies. Its use is indicated in repeated surveys where nonresponse is a problem and strong data dependencies exist. This methodology was developed for the Bureau's Current Employment Statistics Survey but has applications in other repeated surveys.