On the $l_s$-norm Generalization of the NLS method for the Bass model

Authors

  • Dragan Jukic Department of Mathematics, J.J. Strossmayer University of Osijek, Croatia

Keywords:

Bass model, diffusion, $l_s$-norm estimate, least squares estimate, existence problem, data fitting

Abstract

The best-known and widely used model in diffusion research is the Bass model. Estimation of its parameters has been approached in the literature by various methods, among which a very popular one  is the nonlinear least squares (NLS) method proposed by Srinivasan and Mason.
In this paper, we consider the $l_s$-norm $(1\leq s<\infty)$ generalization of the NLS method for the Bass model.

Our focus is on the existence of the corresponding best $l_s$-norm estimate.
We show that it is possible for the best $l_s$-norm estimate not to exist.
As a main result, two theorems on the existence of the best $l_s$-norm estimate are obtained. One of them gives necessary and sufficient conditions
which guarantee the existence of the best $l_s$-norm  estimate.

Author Biography

  • Dragan Jukic, Department of Mathematics, J.J. Strossmayer University of Osijek, Croatia
    Professor of Mathematics

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Published

2017-08-06

Issue

Vol. 6 No. 4: (October 2013)

Section

Mathematical Modeling and Numerical Analysis

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How to Cite

On the $l_s$-norm Generalization of the NLS method for the Bass model. (2017). European Journal of Pure and Applied Mathematics, 6(4), 435-450. https://www.ejpam.com/index.php/ejpam/article/view/1867