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A review of the parameter estimation problem of fitting positive exponential sums to empirical data
Stockholm University, Faculty of Science, Department of Mathematics and Science Education.ORCID iD: 0000-0001-5609-0752
2002 (English)In: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, Vol. 126, no 1, 31-61 p.Article in journal (Refereed) Published
Abstract [en]

Exponential sum models are used frequently: in heat diffusion, diffusion of chemical compounds, time series in medicine, economics, physical sciences and technology. Thus it is important to find good methods for the estimation of parameters in exponential sums. In this paper we review and discuss results from the last forty years of research. There are many different ways of estimating parameters in exponential sums and model a fit criterion, which gives a valid result from the fit. We find that a good choice is a weighted two-norm objective function, with weights based on the maximum likelihood (ML) criterion. If the number of exponential terms is unknown, statistical methods based on an information criterion or cross-validation can be used to determine the optimal number. It is suitable to use hybrid Gauss–Newton (GN) and quasi-Newton algorithms to find the unknown parameters in the constrained weighted nonlinear least-squares (NLLS) problem formulated using an maximal likelihood (ML) objective function. The problem is highly ill conditioned and it is crucial to find good starting values for the parameters. To find the initial parameter values, a modified Prony method or a method based upon rewriting partial sums as geometrical sums is proposed.

Place, publisher, year, edition, pages
Elsevier, 2002. Vol. 126, no 1, 31-61 p.
Keyword [en]
Exponential sums Nonlinear least squares Nonlinear parameter estimation Prony's method Pisarenko's method Compartment models
National Category
Computational Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-147760DOI: 10.1016/S0096-3003(00)00138-7OAI: oai:DiVA.org:su-147760DiVA: diva2:1148671
Available from: 2017-10-12 Created: 2017-10-12 Last updated: 2017-10-12

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