Advanced Modeling and Optimization

Abstract for Paper 1 of Volume 2, Number 3, 2000, pp. 104-121


On a Distribution Free Approach to Analyzing Nonlinear Models


Tanya Fomina
Baltic State Technical University,
St. Petersburg, The 1-st Krasnoarmeyskaya st.
1, St Petersburg, 190000, Russia
E-mail: tvf@brdr.usr.pu.ru
Kenneth Holmström
Applied Optimization and Modeling (TOM),
Center for Mathematical Modeling,
Department of Mathematics and Physics.
Mälardalen University, P.O. Box 883, SE-721 23,
Västerås, Sweden.
E-mail: kenneth.holmstrom@mdh.se
Viatcheslav B. Melas
Faculty of Mathematics and Mechanics,
St. Petersburg State University,
Bibliotechnaya sq., 2, St. Petersburg, 198904, Russia.
E-mail:Viatcheslav.Melas@pobox.math.spbu.ru

Abstract

The nonlinear methods of Least Squares and Maximum Likelihood estimation are the main methods in the theory of nonlinear regression analysis. The serious disadvantage of these methods is that they can be applied only when the distribution of errors is known or is similar to the normal distribution. Using the optimal design theory, we propose an original approach, which is independent of assumptions on errors distribution. This approach is applied to a parameter estimation problem in chemical equilibrium analysis.