By David Roxbee Cox, E. J. Snell
This publication might be of curiosity to senior undergraduate and postgraduate scholars of utilized facts.
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Example text
E. on,unknown parameters not of immediate interest in their own right. Its physical meaning is that it gives the hypothetical frequency distribution of the estimate t if repeat sets of data were obtained under the same conditions and t calculated from each set. We now want to choose a function t(y) such that /T(t;B) is as closely concentrated around Bas possible, whatever may be the true B. Once this is expressed more formally it is a mathematical problem to find a suitable t, subject of course to feasibility of computation.
11) were fitted directly when the origin is remote from the region of values of x covered by the data. 12) would raise no such problems. The general moral is that both for obtaining estimates with errors having simple properties, and for reasons of numerical stability, fitting of models with approximately orthogonalized parameters is advantageous. The details of fitting are thus best carried out in that form, but, as stressed above, the more basic pointS' of interpretation (i) and (ii) may dictate transformation of the results to a reparameterized form.
D) The ability to fit a range of similar data is of great importance in'model choice. It will usually be wise to aim to fit all the sets of data with the same form of model. For instance, if in a number of sets of similar data, some are adequately fitted by straight lines whereas others need to be fitted by parabolas, it will normally be sensible to fit all the sets of data by parabolas, unless some rational explanation can be found for the split into two kinds. (e) Low-degree polynomials can be valuable for interpretation as well as for fitting for interpolation.