Estimation of copolymer reactivity ratios: An example of nonlinear estimation

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Abstract

The first portion of the paper consists of a brief statement of the statistical procedures involved in obtaining efficient estimates of parameters from experimental data, determining their precision, and selecting optimum experiments. Emphasis is primarily directed toward models in which the parameters appear in a nonlinear fashion. Some of the difficulties and pitfalls which are encountered are discussed; primary among these are the problems arising from linearization schemes and transformations affecting the error structure. References are given which supplement the necessarily cursory discussion given here. Utilizing this background, the second half applies itself to the problem of estimating the reactivity ratios in the copolymer equation. Approximate and exact estimation schemes are described which both guarantee most efficient use of the data and allow objective probabilistic statements to be made about the reliability of the estimates. A graph is presented which allows the experimenter to select the two initial feed ratios for his experiments which provide the most information for the estimation scheme. Use of the graph presumes that order of magnitude estimates of the reactivity ratios can be made in advance. A sequential scheme can be followed when prior information is lacking or is not very precise. When more than two different initial feed ratios are to be used, the optimum ratios for two-point experiments give a good indication of the proper range to cover.

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