From marginals to array structure with the Shuttle algorithm

In many statistical problems there is the need to analyze the structure of an unknown n-dimensional array given its marginal distributions. The usual method utilized to solve the problem is linear programming, which involves a large amount of computational time when the original array is large. Alternative solutions have been proposed in the literature, especially to find less time consuming algorithms. One of these is the shuttle algorithm introduced by Buzzigoli and Giusti to calculate lower and upper bounds of the elements of an n-way array, starting from the complete set of its (n-1)-way marginals. The proposed algorithm, very easy to implement with a matrix language, shows interesting properties and possibilities of application. The paper presents the algorithm, analyses its properties and describes its disadvantages. It also suggests possible applications in some statistical fields and, in particular, in Symbolic Data Analysis and, finally, shows the results of some simulations on randomly generated arrays.