A Note on Quadratic Programming in Activation Analysis

Various statistical techniques have been employed in “activation analysis” 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, the usual least squares applications in activation analysis have utilized the ordinary matrix model Y = Xβ + e, 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, the usual applications allow only point estimation, with no provision for confidence intervals and tests for model goodness of fit. Further, the usual applications fail to eliminate the drawback that negative coefficients are sometimes obtained. The present paper sets forth an iterative quadratic programming estimation procedure that not only eliminates the necessity for assumptions (b) and (c), but also alleviates the other above-mentioned difficulties.