An Errors-in-Variables Model in Which Least Squares is Consistent

1973 ◽  
Vol 14 (1) ◽  
pp. 256
Author(s):  
D. J. Aigner
Keyword(s):  
Least Squares ◽  
Errors In Variables

Generalized Least Squares With Ignored Errors in Variables

Technometrics ◽  
2000 ◽  
Vol 42 (4) ◽  
pp. 366-375 ◽  
Author(s):  
Tony Morton-Jones ◽  
Robin Henderson
Keyword(s):  
Least Squares ◽  
Generalized Least Squares ◽  
Errors In Variables

Effects of errors-in-variables on weighted least squares estimation

2014 ◽  
Vol 88 (7) ◽  
pp. 705-716 ◽  
Author(s):  
Peiliang Xu ◽  
Jingnan Liu ◽  
Wenxian Zeng ◽  
Yunzhong Shen
Keyword(s):  
Least Squares ◽  
Weighted Least Squares ◽  
Least Squares Estimation ◽  
Errors In Variables ◽  
Weighted Least Squares Estimation

scholarly journals Modifying Cadzow's algorithm to generate the optimal TLS-solution for the structured EIV-Model of a similarity transformation

2012 ◽  
Vol 2 (2) ◽  
pp. 98-106 ◽  
Author(s):  
B. Schaffrin ◽  
F. Neitzel ◽  
S. Uzun ◽  
V. Mahboub
Keyword(s):  
Least Squares ◽  
Similarity Transformation ◽  
Optimal Solution ◽  
Total Least Squares ◽  
Errors In Variables ◽  
Parameter Adjustment ◽  
Structured Errors

Modifying Cadzow's algorithm to generate the optimal TLS-solution for the structured EIV-Model of a similarity transformationIn 2005, Felus and Schaffrin discussed the problem of a Structured Errors-in-Variables (EIV) Model in the context of a parameter adjustment for a classical similarity transformation. Their proposal, however, to perform a Total Least-Squares (TLS) adjustment, followed by a Cadzow step to imprint the proper structure, would not always guarantee the identity of this solution with the optimal Structured TLS solution, particularly in view of the residuals. Here, an attempt will be made to modify the Cadzow step in order to generate the optimal solution with the desired structure as it would, for instance, also result from a traditional LS-adjustment within an iteratively linearized Gauss-Helmert Model (GHM). Incidentally, this solution coincides with the (properly) Weighted TLS solution which does not need a Cadzow step.

Least Squares Regression Estimates of the Schaefer Production Model: Some Monte Carlo Simulation Results

1980 ◽  
Vol 37 (8) ◽  
pp. 1284-1294 ◽  
Author(s):  
Russell S. Uhler
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Least Squares ◽  
Population Size ◽  
Analytical Methods ◽  
Production Model ◽  
Parameter Estimates ◽  
Errors In Variables ◽  
Least Squares Regression ◽  
Harvest Rate

Both analytical methods and Monte Carlo experiments are used to determine the amount of bias in the regression estimates of the Schaefer model when it is estimated with catch and effort data. It is shown that the use of the catch–effort ratio and effort as regressors leads to the classical errors in variables problem which produces asymptotically biased parameter estimates. Since the seriousness of the bias, and even its direction in the case of certain formulations of the model, cannot be determined by analytical methods, Monte Carlo simulation experiments were used. Four variations of the Schaefer model were investigated; two of which come from a discrete formulation of the model and two of which come from a continuous formulation. The least squares regression estimates of all formulations result in substantial bias although one formulation is considerably better than the others.Bias in the optimal levels of the population size, the harvest rate, and fishing effort are also calculated. It is found that under likely conditions regarding the model equation errors that the optimal population size and harvest rate may be as much as 40–50% in error depending on the model used. In general, however, the bias in these quantities is much smaller than the bias in the parameter estimates themselves.Key words: Schaefer model, Monte Carlo, optimal fishery management, errors in variables, biased estimates

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