Existence of Optimal Weighted Least Squares Estimate for Three-Parametric Exponential Model

2008 ◽  
Vol 37 (9) ◽  
pp. 1383-1398 ◽  
Author(s):  
François Dubeau ◽  
Youness Mir
Keyword(s):  
Least Squares ◽  
Weighted Least Squares ◽  
Exponential Model ◽  
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.

Evaluation for estimating of the PDF and the CDF of Generalized Inverted Exponential Distribution with Application in Industry

2020 ◽  
pp. 507-522
Author(s):  
Parisa Torkaman
Keyword(s):  
Least Squares ◽  
Exponential Distribution ◽  
Mean Squared Error ◽  
Weighted Least Squares ◽  
Real Data ◽  
Minimum Variance ◽  
Cumulative Distribution ◽  
Estimation Methods ◽  
Data Set ◽  
Better Than

The generalized inverted exponential distribution is introduced as a lifetime model with good statistical properties. This paper, the estimation of the probability density function and the cumulative distribution function of with five different estimation methods: uniformly minimum variance unbiased(UMVU), maximum likelihood(ML), least squares(LS), weighted least squares (WLS) and percentile(PC) estimators are considered. The performance of these estimation procedures, based on the mean squared error (MSE) by numerical simulations are compared. Simulation studies express that the UMVU estimator performs better than others and when the sample size is large enough the ML and UMVU estimators are almost equivalent and efficient than LS, WLS and PC. Finally, the result using a real data set are analyzed.

scholarly journals Outlier Detection Algorithms Over Fuzzy Data with Weighted Least Squares

2021 ◽  
Author(s):  
Natalia Nikolova ◽  
Rosa M. Rodríguez ◽  
Mark Symes ◽  
Daniela Toneva ◽  
Krasimir Kolev ◽  
...  
Keyword(s):  
Least Squares ◽  
Outlier Detection ◽  
Weighted Least Squares ◽  
Fuzzy Data ◽  
Detection Algorithms
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