Identifiability and Estimability

Abstract

A general theory of parameter identifiability unbiased decision functions and estimable optimal decision sets is developed covering the usual concepts of identifiability, unbiasedness and estimability. For the estimation of linear parameters in multivariate linear models, the concepts of linear estimability and identifiability coincide, and with a suitable choice of the loss function every linear parameter can be viewed as estimable and identifiable. It is shown, that the condition of reducibility used by H. Bunke to construct a solution of the approgression problem is identifiability of the projection of the unknown regression function on the space of approximating functions.