A GRAS VARIANT SOLVING FOR MINIMUM INFORMATION LOSS

The fundamental idea in Junius and Oosterhaven (2003) is to break down the information contained in the a priori data into two parts: algebraic signs, and absolute values. This approach is well grounded in information theory, and provides a basis on which to solve the problem of adjusting matrices with negative entries. However, Junius and Oosterhaven (2003) have formulated a target function that is not equivalent to the Kullback and Leibler (1951) cross-entropy measure, and so is not a representation of the minimum information loss principle. Neither is the alternative target function proposed by Lenzen et al. (2007). This paper develops the exact Kullback and Leibler cross-entropy measure. In addition, following the constrained optimization approach, this paper applies the same principle to solve adjustment problems where row-sums, column-sums or both are constrained to zero.