On the numerical evaluation of the theoretical variance‐covariance matrix of least squares estimators for echelon‐form varma models

1999 ◽  
Vol 28 (3) ◽  
pp. 743-766
Author(s):  
M. O. Salau
Keyword(s):  
Least Squares ◽  
Covariance Matrix ◽  
Numerical Evaluation ◽  
Least Squares Estimators ◽  
Variance Covariance Matrix

The Solution of Linear Equation Systems

1965 ◽  
Vol 19 (1) ◽  
pp. 78-83
Author(s):  
Peter Wilson
Keyword(s):  
Linear Equation ◽  
Least Squares ◽  
Covariance Matrix ◽  
Error Propagation ◽  
Normal Equations ◽  
The Law ◽  
Linear Equation Systems ◽  
Variance Covariance Matrix

Several methods for solving normal equations in least squares solutions are explained and the variance-covariance matrix is developed from the law of error propagation.

scholarly journals Robust Estimations of Current Velocities with Four-Beam Broadband ADCPs

2009 ◽  
Vol 26 (12) ◽  
pp. 2642-2654 ◽  
Author(s):  
M. Gilcoto ◽  
Emlyn Jones ◽  
Luis Fariña-Busto
Keyword(s):  
Least Squares ◽  
Covariance Matrix ◽  
Least Squares Method ◽  
Weighted Least Squares ◽  
Robust Solution ◽  
Least Squares Solution ◽  
Weighted Least Squares Method ◽  
Radial Beam ◽  
Least Squares Approach ◽  
Variance Covariance Matrix

Abstract An extended explanation of the hypothesis and equations traditionally used to transform between four-beam ADCP radial beam velocities and current velocity components is presented. This explanation includes a dissertation about the meaning of the RD Instrument error velocity and a description of the standard beam-to-current components transformation as a least squares solution. Afterward, the variance–covariance matrix associated with the least squares solution is found. Then, a robust solution for transforming radial beam velocities into current components is derived under the formality of a weighted least squares approach. The associated variance–covariance matrix is also formulated and theoretically proves that the modulus of its elements will be generally lower than the corresponding modulus of the variance–covariance matrix associated with the standard least squares solution. Finally, a comparison between the results obtained using the standard least squares solution and the results of the weighted least squares method, using a high-resolution ADCP dataset, is presented. The results show that, in this case, the weighted least squares solution provides variance estimations that are 4% lower over the entire record period (8 days) and 7% lower during a shorter, more energetic period (12 h).

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.

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