On parameter estimation in the bass model by nonlinear least squares fitting the adoption curve

Darija Marković; Dragan Jukić

International Journal of Applied Mathematics and Computer Science (2013)

  • Volume: 23, Issue: 1, page 145-155
  • ISSN: 1641-876X

Abstract

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The Bass model is one of the most well-known and widely used first-purchase diffusion models in marketing research. Estimation of its parameters has been approached in the literature by various techniques. In this paper, we consider the parameter estimation approach for the Bass model based on nonlinear weighted least squares fitting of its derivative known as the adoption curve. We show that it is possible that the least squares estimate does not exist. As a main result, two theorems on the existence of the least squares estimate are obtained, as well as their generalization in the ls norm (1 ≤ s < ∞). One of them gives necessary and sufficient conditions which guarantee the existence of the least squares estimate. Several illustrative numerical examples are given to support the theoretical work.

How to cite

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Darija Marković, and Dragan Jukić. "On parameter estimation in the bass model by nonlinear least squares fitting the adoption curve." International Journal of Applied Mathematics and Computer Science 23.1 (2013): 145-155. <http://eudml.org/doc/251327>.

@article{DarijaMarković2013,
abstract = {The Bass model is one of the most well-known and widely used first-purchase diffusion models in marketing research. Estimation of its parameters has been approached in the literature by various techniques. In this paper, we consider the parameter estimation approach for the Bass model based on nonlinear weighted least squares fitting of its derivative known as the adoption curve. We show that it is possible that the least squares estimate does not exist. As a main result, two theorems on the existence of the least squares estimate are obtained, as well as their generalization in the ls norm (1 ≤ s < ∞). One of them gives necessary and sufficient conditions which guarantee the existence of the least squares estimate. Several illustrative numerical examples are given to support the theoretical work.},
author = {Darija Marković, Dragan Jukić},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {Bass model; least squares estimate; existence problem; data fitting; bass model},
language = {eng},
number = {1},
pages = {145-155},
title = {On parameter estimation in the bass model by nonlinear least squares fitting the adoption curve},
url = {http://eudml.org/doc/251327},
volume = {23},
year = {2013},
}

TY - JOUR
AU - Darija Marković
AU - Dragan Jukić
TI - On parameter estimation in the bass model by nonlinear least squares fitting the adoption curve
JO - International Journal of Applied Mathematics and Computer Science
PY - 2013
VL - 23
IS - 1
SP - 145
EP - 155
AB - The Bass model is one of the most well-known and widely used first-purchase diffusion models in marketing research. Estimation of its parameters has been approached in the literature by various techniques. In this paper, we consider the parameter estimation approach for the Bass model based on nonlinear weighted least squares fitting of its derivative known as the adoption curve. We show that it is possible that the least squares estimate does not exist. As a main result, two theorems on the existence of the least squares estimate are obtained, as well as their generalization in the ls norm (1 ≤ s < ∞). One of them gives necessary and sufficient conditions which guarantee the existence of the least squares estimate. Several illustrative numerical examples are given to support the theoretical work.
LA - eng
KW - Bass model; least squares estimate; existence problem; data fitting; bass model
UR - http://eudml.org/doc/251327
ER -

References

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