Parameter Estimation and Nonlinear Least-Squares Methods

2018 ◽  
pp. 103-124
Author(s):  
Michael Y. Li
Keyword(s):  
Parameter Estimation ◽  
Least Squares ◽  
Nonlinear Least Squares

Integrating Parameter Estimation Solutions From the Time and Time-Scale Domains

2009 ◽  
Author(s):  
James R. McCusker ◽  
Kourosh Danai
Keyword(s):  
Parameter Estimation ◽  
Least Squares ◽  
Time Scale ◽  
Prediction Error ◽  
Nonlinear Least Squares ◽  
Integrated Approach ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Single Model ◽  
Iterative Estimation

A method of parameter estimation was recently introduced that separately estimates each parameter of the dynamic model [1]. In this method, regions coined as parameter signatures, are identified in the time-scale domain wherein the prediction error can be attributed to the error of a single model parameter. Based on these single-parameter associations, individual model parameters can then be estimated for iterative estimation. Relative to nonlinear least squares, the proposed Parameter Signature Isolation Method (PARSIM) has two distinct attributes. One attribute of PARSIM is to leave the estimation of a parameter dormant when a parameter signature cannot be extracted for it. Another attribute is independence from the contour of the prediction error. The first attribute could cause erroneous parameter estimates, when the parameters are not adapted continually. The second attribute, on the other hand, can provide a safeguard against local minima entrapments. These attributes motivate integrating PARSIM with a method, like nonlinear least-squares, that is less prone to dormancy of parameter estimates. The paper demonstrates the merit of the proposed integrated approach in application to a difficult estimation problem.

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.

Powell’s method-based nonlinear least-squares data fitting for the Mittag-Leffler relaxation function

2015 ◽  
Vol 22 (5) ◽  
pp. 1058-1067
Author(s):  
Changqing Fang ◽  
Huiyu Sun ◽  
Jianping Gu
Keyword(s):  
Parameter Estimation ◽  
Least Squares ◽  
Relaxation Function ◽  
Nonlinear Least Squares ◽  
Data Fitting ◽  
Direct Search ◽  
Search Method ◽  
Direct Search Method ◽  
Viscoelastic Models

The Mittag-Leffler relaxation function, [Formula: see text], with [Formula: see text], plays an important role in the fractional viscoelastic models. The Mittag-Leffler function is an infinite series whose analytic derivatives are unexplored, thus a direct search method based on Powell’s method is introduced to solve the minimization problem of nonlinear least-squares data fitting for Mittag-Leffler relaxation function in this paper. A simple and effective method is provided for the determination of the initial values and an acceleration strategy is proposed for this direct search method. Numerical results show this direct search method is efficient in the parameter estimation of the Mittag-Leffler relaxation function. Furthermore, the acceleration strategy proves to be conducive to improving the computational efficiency of this direct search method.

Surface fitting and parameter estimation with nonlinear least squares

1995 ◽  
Vol 5 (3) ◽  
pp. 247-269 ◽  
Author(s):  
Mårten Gulliksson ◽  
Inge Söderkvist
Keyword(s):  
Parameter Estimation ◽  
Least Squares ◽  
Nonlinear Least Squares ◽  
Surface Fitting
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