Statistical techniques in activation analysis

Technical methods involved in activation analysis have received widespread publicity during recent years. Even more recently, various statistical techniques have been employed in conjunction with such technical methods in order to provide a better means of estimating the amounts of various pure chemical elements contained in an unknown mixture. In particular, the method of “least squares” has been employed extensively. However, for the most part, usual least squares applications in activation analysis have utilized the ordinary matrix model Y = Xβ +ρ, under the “error” assumptions (a) zero means, (b) variances proportional to Y and (c) zero covariances. In addition to the fact that assumptions (b) and (c) may lead to erroneous results, previous applications allow only point estimation, with no provision for confidence intervals and tests for model goodness of fit. The present paper is concerned with a feasible iterative estimation procedure which eliminates the necessity for assumptions (b) and (c), and which allows construction of confidence intervals and a test for model goodness of fit. A numerical example of the application of the technique is included. Further, an indication is given of how the technique can be extended to apply in the case of “restricted” least squares (quadratic programming).