Neyman Measurement and Prediction Procedures

Abstract Consider the following two situations which are characteristic for the application of statistical procedures. 1.) There is a deterministic variable of interest , whose actual value θ ∈ Θ is unknown. 2.) There is a random variable of interest with uncertain outcome . The aim in the first situation is to determine the unknown actual value θ of the quantity of interest . In the second situation the aim is to make a prediction about the uncertain outcome of the random variable of interest . Thus, measurement procedure and a prediction procedures are needed. In this paper it is shown that appropriately defined the two problems are equivalent in the sense that any solution of the one problem implies a solution of the second problem. Moreover, a quality indicator is derived reflecting the degree of “fitness for use” of a given procedure and enabling definition and determination of “optimal” statistical procedures. In agreement with general scientific practice, but in contrast to traditional statistics, the measurement and prediction procedures are developed for a suitably specified bounded range for the admissible values of the deterministic variable .