An independence transformation in decision theory

Abstract

In near real time accountancy, a sequence of material balance statistics is used in order to make a statement after each inventory period whether or not material has been lost or diverted during this period. Since these statistics, however, are correlated via the intermediate real inventories, one applies a linear transformation such that the transformed statistics are uncorrelated and therefore, since normal, independent. This transformation was introduced by K. B. Stewart [Technometrics 12, 247-258 (1970; Zbl 0211.50005)] who constructed a minimum variance unbiased estimate for the starting inventory of an inventory period with the help of the book and real inventories of the previous period. Since that time, various approaches have been discussed. It is the purpose of this contribution to present these approaches and to compare their relative advantages.