GM(1,1) Model Based on Least Absolute Estimation of Residual

2011 ◽  
Vol 90-93 ◽  
pp. 2881-2886
Author(s):  
Yong He Deng
Keyword(s):  
Least Squares ◽  
Least Squares Estimation ◽  
Absolute Value ◽  
Model Based ◽  
Gross Error

Based on the choice characteristic of least absolute estimation ,and the principle of the minimum of summation of residual absolute value,the GM(1,1) model is proposed to distortion inspecting and forecasting.Exemples show the precision of least absolute estimation is uncertain to be higher a little than that of least squares estimation when observation value contains gross error,and the precision of least absolute estimation is lower a little than that of least squares estimation when observation value doesn’t contain gross error.So least absolute estimation isn’t beter to GM(1,1).

Parameter Estimation for a Multiplicative Competitive Interaction Model—Least Squares Approach

1974 ◽  
Vol 11 (3) ◽  
pp. 303-311 ◽  
Author(s):  
Masao Nakanishi ◽  
Lee G. Cooper
Keyword(s):  
Parameter Estimation ◽  
Least Squares ◽  
Interaction Model ◽  
Multiplicative Model ◽  
Competitive Interaction ◽  
Least Squares Estimation ◽  
Potential Usefulness ◽  
Estimation Techniques ◽  
Model Based ◽  
Least Squares Approach

Least squares estimation techniques are developed for a special multiplicative model based on the Luce choice axiom whose potential usefulness in marketing applications justifies estimation techniques which can be easily implemented.

scholarly journals A New Reliability Model Based on Lindley Distribution with Application to Failure Data

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Norah N. Al-Mutairi ◽  
Lutfiah I. Al-Turk ◽  
Sharifah A. Al-Rajhi
Keyword(s):  
Least Squares ◽  
Software Reliability ◽  
Nonlinear Least Squares ◽  
Least Squares Estimation ◽  
Lindley Distribution ◽  
New Model ◽  
Reliability Models ◽  
Model Based ◽  
Failure Data ◽  
Nonlinear Least Squares Estimation

Software reliability is an important feature that influences systems’ reliability. Software reliability models are a common tool to evaluate software reliability quantitatively. Various reliability models have been suggested based on the NHPP (nonhomogeneous Poisson process). In this article, a new NHPP model based on the Lindley distribution is proposed. The mathematical formulas for its measures of reliability are obtained and graphically illustrated. The proposed model’s parameters are estimated using both the NLSE (nonlinear least squares estimation) and the WNLSE (weighted nonlinear least squares estimation) methods. The model is then validated based on several different reliability datasets. The methods of estimation are evaluated and compared using three different criteria. The performance of the new model is also evaluated and compared, both objectively and subjectively, with three previously suggested models. The application results show that our new model demonstrates good performance in our selected failure data.

The Estimation of Blood Platelet Survival

1972 ◽  
Vol 28 (03) ◽  
pp. 447-456 ◽  
Author(s):  
E. A Murphy ◽  
M. E Francis ◽  
J. F Mustard
Keyword(s):  
Standard Deviation ◽  
Least Squares ◽  
Experimental Error ◽  
Blood Platelet ◽  
Least Squares Estimation ◽  
Systematic Relationship ◽  
Platelet Survival ◽  
The Mean ◽  
Normally Distributed

SummaryThe characteristics of experimental error in measurement of platelet radioactivity have been explored by blind replicate determinations on specimens taken on several days on each of three Walker hounds.Analysis suggests that it is not unreasonable to suppose that error for each sample is normally distributed ; and while there is evidence that the variance is heterogeneous, no systematic relationship has been discovered between the mean and the standard deviation of the determinations on individual samples. Thus, since it would be impracticable for investigators to do replicate determinations as a routine, no improvement over simple unweighted least squares estimation on untransformed data suggests itself.

Least Squares Estimation in Uncertain Differential Equations

2020 ◽  
Vol 28 (10) ◽  
pp. 2651-2655 ◽  
Author(s):  
Yuhong Sheng ◽  
Kai Yao ◽  
Xiaowei Chen
Keyword(s):  
Differential Equations ◽  
Least Squares ◽  
Least Squares Estimation
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