Applications of Transportation Theory to Statistical Problems

The two-dimensional controlled selection problem and the problem of maximizing the overlap of old and new primary sampling units after restratification and change of selection probabilities have been studied for several decades but have never been completely solved until now. Using transportation theory, complete solutions are obtained here for these and other problems. The solution to the controlled selection problem is based on a specific transportation model that was originally developed, in a previous paper by Cox and Ernst (1982), to solve completely the controlled rounding problem, namely the problem of optimally rounding real-valued entries in a two-way tabular array to adjacent integer values in a manner that preserves the tabular (additive) structure of the array. This model is also applied to other statistical problems, such as raking and statistical disclosure for frequency count tabulations and microdata.