Theoretical and Computative Difficulties of Modern Non-linear Regression Analysis
by
Yuri V. Chebrakov
Saint-Petersburg State Technical University

In this work, a set of modern non-linear regression analysis techniques, designed especially for solving approximation type problems is investigated. It is demonstrated that the application of all these models and algorithms leads to arising series of theoretical and computative difficulties, which are mainly explained by the fact that modern statements of non-linear regression analysis problems are too far from real experimental situations. In particular, up to the present these statements make no allowance for facts [1 - 4] that (a) results of calculations may be depended on the way, by which the investigated data are obtained; (b) the given accuracy of calculated values is not to be computed for data, measured with high level of errors; (c) a single solution of the non-linear regression analysis problems for contaminated data arrays is wrong one; and others. To overcome series of the discussed theoretical and computative difficulties, we suggest to implant the measurement function g, allowing to describe the way of dependent variable measurement, in non-linear fitting models and to use a set of methods, concepts and determinations from the continious variant of estimation theory [1, 2]. It should be noted, in some experimental situations, methods of the continuous variant of estimation theory are converted to a set of iterative lot-work-of-time procedures and so they are inexecutable in practice. We give detailed description of all such experimental situations and describe also a set of methods, allowing to find correct solutions of non-linear fitting problems in these situations. References: 1. Chebrakov Y.V., The parameters estimation theory in the measuring experiments. St.-Petersburg, St.-Petersburg State University Press, 1997. 2. Chebrakov Y.V. and Shmagin V.V., Regression data analysis for physicists and chemists. St.-Petersburg, St.-Petersburg State University Press, 1998. 3. Chebrakov Y.V. and Shmagin V.V., Computative paradoxes in modern data analysis. Smarandache Notions J. (1999) Vol.10. (1-2-3) 61-80. 4. Kalman R., Identificating noise systems. J. Uspechi matematich. nauk. (1985) Vol.40. (4) 27-41

Date received: January 14, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadd-32.