Processing results of non-linear regression experiments with hetrogeneous objects
by
Vladimir V. Shmagin
Saint-Petersburg State Aerospace Instrumentation University

Let us suppose for non-linear regression experiments with heterogeneous objects that the data analysis model has form Y = g(F(A, X) + W(D, X) + E), (1) where Y is dependent variable; F(A, X) is a given non-linear approximative function; W(D, X) is unknown approximative function, having finite value on the given experiment realisation {X}; E is random variable; g is a function, allowing to describe the way of dependent variable measurement. Thus, (1) differs from the data analysis model, used in the continuous variant of estimation theory [1, 2], in the presence of the function W(D, X), by which, in particular, one may simulate an influence of the object heterogeneity on researching properties. For the sake of simplicity we will assume in this work, that the main non-linear estimation problem in experiments with heterogeneous objects is to determine a form of the function W(D, X). Thus, the main goal of this report is to elaborate the methods on revealing the form of the function W(D, X), describing the influence of object heterogeneit on its investigated properties. Two simple cases are discussed: (1) when the non-linear approximative function G(B, X) differs from the initial (postulated) function F(A, X) in an additive term W(D, X) and (2) when the contribution of the function W(D, X) in investigated properties of object leads to local-inadequacy of initial fitting function F(A, X).

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.

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-34.