A GRAS VARIANT SOLVING FOR MINIMUM INFORMATION LOSS

Abstract

The fundamental idea in Junius and Oosterhaven (2003) Junius, T. and Oosterhaven, J. 2003. The Solution of Updating or Regionalizing a Matrix with both Positive and Negative Entries. Economic Systems Research, 15: 87–96. [Taylor & Francis Online] , [Google Scholar] 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) Junius, T. and Oosterhaven, J. 2003. The Solution of Updating or Regionalizing a Matrix with both Positive and Negative Entries. Economic Systems Research, 15: 87–96. [Taylor & Francis Online] , [Google Scholar] have formulated a target function that is not equivalent to the Kullback and Leibler (1951) Kullback, S. and Leibler, R. A. 1951. On Information and Sufficiency. Annals of Mathematical Statistics, 4: 99–111. [Google Scholar] 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) Lenzen, M., Wood, R. and Gallego, B. 2007. Some Comments on the GRAS Method. Economic Systems Research, 19: 461–465. [Taylor & Francis Online] , [Google Scholar]. 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.