Knowledge that Transforms

THE TASK OF estimating the components, i.e., parameters and distributions, of a stochastic structure and the companion problem of identification have been treated in a series of papers in the last few years. Impetus to research in this sphere was given by the work of Reiersol [2] which appeared in a 1950 issue of Econometrica. Recently, Wolfowitz [3] has shown that strongly consistent estimators may be obtained by the method of minimum distance for various structures when the components are identifiable. This raises anew the desirability of specifying under what conditions the more important structures are identifiable. Suppose that an observable chance variable X is known to be representable by the stochastic difference equation (structure) Xi = Ui + aUll where the chance variables Ui are independent and identically distributed. If we consider a pair of observables