A Conditional Generalized Least Squares Method for Estimating the Size of a Closed Population

1989 ◽  
Vol 46 (5) ◽  
pp. 818-823 ◽  
Author(s):  
R. N. Crittenden ◽  
G. L Thomas
Keyword(s):  
Least Squares ◽  
Population Size ◽  
Sockeye Salmon ◽  
Structural Model ◽  
Least Squares Method ◽  
Generalized Least Squares ◽  
Minimum Variance ◽  
Linear Estimator ◽  
Dispersion Matrix ◽  
Catch Per Unit Effort

In the corrected Leslie–DeLury catch-per-unit-effort method, estimation of the corrected cumulative catches causes the underlying model to be an errors-in-covariates structural model with a nondiagonal dispersion matrix. This violates the assumptions of regression and causes the corrected Leslie–DeLury method to give biased estimates of the population size and its variance. We use generalized least squares and a controlled variables design to resolve these difficulties, obtain the minimum-variance unbiased linear estimator, and compute unbiased variance estimates. We apply our method to sockeye salmon fingerlings (Oncorhynchus nerka) netted in a hatchery pond. For these data, arranged according to the controlled variables design, the corrected Leslie–DeLury method underestimates the standard error of the population size by 41%.

scholarly journals Minimum variance-embedded deep kernel regularized least squares method for one-class classification and its applications to biomedical data

2020 ◽  
Vol 123 ◽  
pp. 191-216 ◽  
Author(s):  
Chandan Gautam ◽  
Pratik K. Mishra ◽  
Aruna Tiwari ◽  
Bharat Richhariya ◽  
Hari Mohan Pandey ◽  
...  
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Minimum Variance ◽  
Biomedical Data ◽  
Regularized Least Squares ◽  
One Class Classification

Harmonizing biomass tables by generalized least squares

1985 ◽  
Vol 15 (2) ◽  
pp. 331-340 ◽  
Author(s):  
T. Cunia ◽  
R. D. Briggs
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Weighted Least Squares ◽  
Regression Function ◽  
Generalized Least Squares ◽  
Ordinary Least Squares ◽  
Sample Tree ◽  
Tree Data ◽  
Regression Techniques ◽  
Ordinary Least Squares Method

To construct biomass tables for various tree components that are consistent with each other, one may use linear regression techniques with dummy variables. When the biomass of these components is measured on the same sample trees, one should also use the generalized rather than ordinary least squares method. A procedure is shown which allows the estimation of the covariance matrix of the sample biomass values and circumvents the problem of storing and inverting large covariance matrices. Applied to 20 sets of sample tree data, the generalized least squares regressions generated estimates which, on the average were slightly higher (about 1%) than the sample data. The confidence and prediction bands about the regression function were wider, sometimes considerably wider than those estimated by the ordinary weighted least squares.

The least-squares intersection of a family of lines and its application to phase equilibria

1982 ◽  
Vol 60 (15) ◽  
pp. 1978-1981 ◽  
Author(s):  
John W. Lorimer
Keyword(s):  
Phase Equilibria ◽  
Least Squares ◽  
Least Squares Method ◽  
Solid Phase ◽  
Generalized Least Squares ◽  
First Approximation ◽  
Generalized Least Squares Method ◽  
Point Of Intersection ◽  
Straight Lines ◽  
General Method

A generalized least-squares method is described for finding the point of intersection of a family of straight lines, each of which is defined by two experimental points. It is shown that the method of the least-squares triangle (Can. J. Chem. 59, 3076 (1981)) is a good first approximation to the general method. An example demonstrates the method of iteration of both parameters and observations for a problem involving evaluation of solid phase compositions from solubility measurements.

Generalized Least Squares Method, Heteroskedasticity, and Multivariate Regression

2012 ◽  
pp. 179-212
Author(s):  
Jean-Pierre Florens ◽  
Velayoudom Marimoutou ◽  
Anne Peguin-Feissolle ◽  
Josef Perktold ◽  
Marine Carrasco
Keyword(s):  
Least Squares ◽  
Multivariate Regression ◽  
Least Squares Method ◽  
Generalized Least Squares ◽  
Generalized Least Squares Method

scholarly journals Generalized Inequalities to Optimize the Fitting Method for Track Reconstruction

Physics ◽  
2020 ◽  
Vol 2 (4) ◽  
pp. 608-623
Author(s):  
Gregorio Landi ◽  
Giovanni E. Landi
Keyword(s):  
Least Squares ◽  
Minimum Variance ◽  
Linear Estimator ◽  
Track Reconstruction ◽  
Gaussian Distributions ◽  
Least Squares Estimators ◽  
Optimal Estimator ◽  
Fitting Method ◽  
Optimal Estimators ◽  
The One

A standard criterium in statistics is to define an optimal estimator as the one with the minimum variance. Thus, the optimality is proved with inequality among variances of competing estimators. The demonstrations of inequalities among estimators are essentially based on the Cramer, Rao and Frechet methods. They require special analytical properties of the probability functions, globally indicated as regular models. With an extension of the Cramer–Rao–Frechet inequalities and Gaussian distributions, it was proved the optimality (efficiency) of the heteroscedastic estimators compared to any other linear estimator. However, the Gaussian distributions are a too restrictive selection to cover all the realistic properties of track fitting. Therefore, a well-grounded set of inequalities must overtake the limitations to regular models. Hence, the inequalities for least-squares estimators are generalized to any model of probabilities. The new inequalities confirm the results obtained for the Gaussian distributions and generalize them to any irregular or regular model. Estimators for straight and curved tracks are considered. The second part deals with the shapes of the distributions of simplified heteroscedastic track models, reconstructed with optimal estimators and the standard (non-optimal) estimators. A comparison among the distributions of these different estimators shows the large loss in resolution of the standard least-squares estimators.

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