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Showing papers by "Herman Chernoff published in 1999"


Journal ArticleDOI
TL;DR: Among other results, this paper demonstrated that, asymptotically, locally optimal designs for estimating one parameter require the use of no more than k of the available experiments, when the distribution of the data from these experiments involves k unknown parameters.
Abstract: During my visit at Stanford University in the summer and fall of 1951, some problems proposed by the National Security Agency (NSA) for an Office of Naval Research (ONR) applied research grant led to two of my publications [1, 2] which had a profound effect on my future research. Both papers had relevance to issues in experimental design. One of these concerned optimal design for estimation. Among other results, it demonstrated that, asymptotically, locally optimal designs for estimating one parameter require the use of no more than k of the available experiments, when the distribution of the data from these experiments involves k unknown parameters. A trivial example would be that to estimate the slope of a straight line regression with constant variance, where the explanatory variable x is confined to the interval [-1, 1], an optimal design requires observations concentrated at the two ends, x = 1 and x = -1. Shortly after I derived this result, I discovered a related publication by Gustav Elfving [3]. While Elfving's result is restricted to k-dimensional regression experiments, it gives an elegant geometrical representation of the optimal design accompanied by an equally elegant derivation, which I still find pleasure in presenting to audiences who are less acquainted with this paper than they should be. In some problems, practical considerations make it impossible to apply optimal designs. One beauty of the Elfving result is that the graphical representation of his result makes it rather clear how much is lost by applying some restricted suboptimal methods, and gives some guidance to wise compromises between optimality and practicality. By 1950, experimental design was a wellestablished field of statistics. Major sources of application were in agriculture and chemistry, and

15 citations