On the $l_s$-norm Generalization of the NLS method for the Bass model
Keywords:
Bass model, diffusion, $l_s$-norm estimate, least squares estimate, existence problem, data fittingAbstract
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.
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Published
2017-08-06
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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