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.

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 Extended Peridynamics and Parameter Optimization Study Based on Moving Least Squares Method

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Jingwei Xu ◽  
Wei Hou ◽  
Shoucheng Luan ◽  
Shuting Mao ◽  
Guowei Liu ◽  
...  
Keyword(s):  
Weight Function ◽  
Least Squares ◽  
Least Squares Method ◽  
Moving Least Squares ◽  
Weight Functions ◽  
Optimization Study ◽  
Fitting Method ◽  
Moving Least Squares Method ◽  
Physical Information ◽  
The One

Based on the theory of peridynamics, the least squares and the moving least squares method are proposed to fit the physical information at nondiscrete points. It makes up for the shortcomings of the peridynamic method that only solves the discrete nodes and cannot obtain the physical information of other blank areas. The extended method is used to fit the one-way vibration problem of the rod, and the curve of the displacement of a nondiscrete node in the rod is extracted with time. The fitted displacement results are compared with the theoretical results to verify the feasibility of the fitting method. At the same time, the parameters in the fitting of the moving least squares method are optimized, and the effects of different tight weight functions and influence ranges on the results are analyzed. The results show that when the weight function is a power exponential function, the fitting effect increases with the decrease in the coefficient. When the weight function is a cubic spline weight function, a better fitting effect is obtained. And in the case of ensuring the fitting result, the affected area should be reduced as much as possible, and the calculation efficiency and precision can be improved.

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.

Theoretical accuracy of the last squares method in the isotope dilution analysis

1984 ◽  
Vol 49 (4) ◽  
pp. 805-820
Author(s):  
Ján Klas
Keyword(s):  
Least Squares ◽  
Isotope Dilution ◽  
Least Squares Method ◽  
Isotope Dilution Analysis ◽  
Straight Line ◽  
The One ◽  
Two Parameter ◽  
Theoretical Accuracy

The accuracy of the least squares method in the isotope dilution analysis is studied using two models, viz a model of a two-parameter straight line and a model of a one-parameter straight line.The equations for the direct and the inverse isotope dilution methods are transformed into linear coordinates, and the intercept and slope of the two-parameter straight line and the slope of the one-parameter straight line are evaluated and treated.

scholarly journals A New Inverted Topp-Leone Distribution: Applications to the COVID-19 Mortality Rate in Two Different Countries

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 25 ◽  
Author(s):  
Ehab Almetwally ◽  
Randa Alharbi ◽  
Dalia Alnagar ◽  
Eslam Hafez
Keyword(s):  
Statistical Model ◽  
Least Squares ◽  
Weighted Least Squares ◽  
Likelihood Estimation ◽  
Linear Representation ◽  
Rate Function ◽  
Estimation Methods ◽  
Unknown Parameters ◽  
Least Squares Estimators ◽  
New Distribution

This paper aims to find a statistical model for the COVID-19 spread in the United Kingdom and Canada. We used an efficient and superior model for fitting the COVID 19 mortality rates in these countries by specifying an optimal statistical model. A new lifetime distribution with two-parameter is introduced by a combination of inverted Topp-Leone distribution and modified Kies family to produce the modified Kies inverted Topp-Leone (MKITL) distribution, which covers a lot of application that both the traditional inverted Topp-Leone and the modified Kies provide poor fitting for them. This new distribution has many valuable properties as simple linear representation, hazard rate function, and moment function. We made several methods of estimations as maximum likelihood estimation, least squares estimators, weighted least-squares estimators, maximum product spacing, Crame´r-von Mises estimators, and Anderson-Darling estimators methods are applied to estimate the unknown parameters of MKITL distribution. A numerical result of the Monte Carlo simulation is obtained to assess the use of estimation methods. also, we applied different data sets to the new distribution to assess its performance in modeling data.

On the admissibility of restricted least squares estimators

1984 ◽  
Vol 13 (9) ◽  
pp. 1135-1146 ◽  
Author(s):  
Ron C. Mittelhammer ◽  
Roger K. Conway
Keyword(s):  
Least Squares ◽  
Least Squares Estimators
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