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

Darija Markovic, D. Jukić
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引用次数: 10

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.
采用非线性最小二乘拟合采用曲线的低音模型参数估计
Bass模型是市场研究中最著名、应用最广泛的首次购买扩散模型之一。其参数的估计已在文献中通过各种技术进行了探讨。在本文中,我们考虑了基于非线性加权最小二乘拟合的Bass模型的参数估计方法,即采用曲线的导数。我们证明了最小二乘估计可能不存在。得到了两个关于最小二乘估计存在性的定理,以及它们在ls范数(1≤s <∞)下的推广。其中给出了保证最小二乘估计存在的充分必要条件。文中给出了几个数值实例来支持理论工作。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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