Exact Solution of an Approximate Weighted Least Squares Estimate of Energy-Based Source Localization in Sensor Networks

2015 ◽  
Vol 64 (10) ◽  
pp. 4645-4654 ◽  
Author(s):  
Jianhua Yuan ◽  
Wenbao Ai ◽  
Huijun Deng ◽  
Tianping Shuai ◽  
Xinchao Zhao
Keyword(s):  
Exact Solution ◽  
Sensor Networks ◽  
Least Squares ◽  
Source Localization ◽  
Weighted Least Squares ◽  
Least Squares Estimate ◽  
Weighted Least Squares Estimate

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

2013 ◽  
Vol 23 (1) ◽  
pp. 145-155 ◽  
Author(s):  
Darija Marković ◽  
Dragan Jukić
Keyword(s):  
Parameter Estimation ◽  
Least Squares ◽  
Weighted Least Squares ◽  
Sufficient Conditions ◽  
Marketing Research ◽  
Nonlinear Least Squares ◽  
Theoretical Work ◽  
Bass Model ◽  
Least Squares Fitting ◽  
Least Squares Estimate

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.

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