Multivariate Prediction: Selection of the Most Informative Components to Measure

Abstract

A number of interesting problems in the design of experiments, such as sensor allocation, selection of sites for the observing stations, determining sampler positions in traffic monitoring, and which variables to survey/measure in sampling studies, may be considered in the following setting. Given the covariance matrix of a multi-dimensional random vector and given the ratio of the number of possible observations to the observational error, select those components which must be observed to guarantee minimization of an objective function describing the quality of prediction of all or prescribed components. We show that the problem can be considered in the framework of convex design theory and derive some simple but effective algorithms for the selection of an optimal subset of components to be observed.