scholarly journals Modifying Two-Parameter Ridge Liu Estimator Based on Ridge Estimation

2019 ◽  
pp. 881-890
Author(s):  
Tarek Mahmoud Omara
Keyword(s):  
Simulation Study ◽  
Mean Squared Error ◽  
Error Matrix ◽  
Liu Estimator ◽  
Mean Squared Error Matrix ◽  
Ridge Estimation ◽  
Squared Error ◽  
The Mean ◽  
Two Parameter

In this paper, we introduce the new biased estimator to deal with the problem of multicollinearity. This estimator is considered a modification of Two-Parameter Ridge-Liu estimator based on ridge estimation. Furthermore, the superiority of the new estimator than Ridge, Liu and Two-Parameter Ridge-Liu estimator were discussed. We used the mean squared error matrix (MSEM) criterion to verify the superiority of the new estimate.  In addition to, we illustrated the performance of the new estimator at several factors through the simulation study.

scholarly journals Stochastic Restricted Liu Type estimator for SUR model

2018 ◽  
pp. 903-911
Author(s):  
Tarek Mahmoud Omara
Keyword(s):  
Simulation Study ◽  
Mean Squared Error ◽  
Error Matrix ◽  
Mean Squared Error Matrix ◽  
Squared Error ◽  
Restricted Estimator

In this paper, we introduce new Stochastic Restricted Estimator for SUR model, defined by Stochastic  Restricted Liu Type  SUR estimator (SRLTSE) . The propose estimator has deal with multicollinearity in SUR model if there is a degree of uncertainty in the parameters restriction. Moreover, the superiority of (SRLTSE) estimator  was derived with respect to mean squared error matrix (MSEM) criteria. Finally, a simulation study was conducted. This simulation used standard mean squares error  (MSE) criterion to illustrate the advantage between Stochastic  Restricted SUR estimator (SRSE), Stochastic  Restricted Ridge SUR estimator (SRRSE), and Stochastic  Restricted Liu Type  SUR estimator (SRLTSE) at several factors. 

scholarly journals Efficient computation of the Nagaoka–Hayashi bound for multiparameter estimation with separable measurements

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Lorcán O. Conlon ◽  
Jun Suzuki ◽  
Ping Koy Lam ◽  
Syed M. Assad
Keyword(s):  
Finite Number ◽  
Mean Squared Error ◽  
Efficient Computation ◽  
Error Matrix ◽  
Mean Squared Error Matrix ◽  
Multiple Parameters ◽  
Squared Error ◽  
The Mean ◽  
Cramer Rao Bound ◽  
Physical Quantities

AbstractFinding the optimal attainable precisions in quantum multiparameter metrology is a non-trivial problem. One approach to tackling this problem involves the computation of bounds which impose limits on how accurately we can estimate certain physical quantities. One such bound is the Holevo Cramér–Rao bound on the trace of the mean squared error matrix. The Holevo bound is an asymptotically achievable bound when one allows for any measurement strategy, including collective measurements on many copies of the probe. In this work, we introduce a tighter bound for estimating multiple parameters simultaneously when performing separable measurements on a finite number of copies of the probe. This makes it more relevant in terms of experimental accessibility. We show that this bound can be efficiently computed by casting it as a semidefinite programme. We illustrate our bound with several examples of collective measurements on finite copies of the probe. These results have implications for the necessary requirements to saturate the Holevo bound.

scholarly journals Two Different Classes of Shrinkage Estimators for the Scale Parameter of the Rayleigh Distribution

2021 ◽  
Vol 19 (1) ◽  
pp. 2-21
Author(s):  
Talha Omer ◽  
Zawar Hussain ◽  
Muhammad Qasim ◽  
Said Farooq Shah ◽  
Akbar Ali Khan
Keyword(s):  
Simulation Study ◽  
Mean Squared Error ◽  
Scale Parameter ◽  
Rayleigh Distribution ◽  
Shrinkage Estimators ◽  
Unbiased Estimators ◽  
Squared Error ◽  
The Mean ◽  
Simulation Results

Shrinkage estimators are introduced for the scale parameter of the Rayleigh distribution by using two different shrinkage techniques. The mean squared error properties of the proposed estimator have been derived. The comparison of proposed classes of the estimators is made with the respective conventional unbiased estimators by means of mean squared error in the simulation study. Simulation results show that the proposed shrinkage estimators yield smaller mean squared error than the existence of unbiased estimators.

The Sailor-diagram. An extension of the Taylor diagram to two-dimensional variables for verification of model data.

2020 ◽  
Author(s):  
Jon Saenz ◽  
Sheila Carreno-Madinabeitia ◽  
Ganix Esnaola ◽  
Santos J. González-Rojí ◽  
Gabriel Ibarra-Berastegi ◽  
...  
Keyword(s):  
Time Series ◽  
Wind Velocity ◽  
Mean Squared Error ◽  
Cmip5 Models ◽  
Two Dimensional ◽  
Error Matrix ◽  
Squared Error ◽  
Taylor Diagram ◽  
The Mean ◽  
The Individual

<p align="justify">A new diagram is proposed for the verification of vector quantities generated by individual or multiple models against a set of observations. It has been designed with the idea of extending the Taylor diagram to two-dimensional vector such as currents, wind velocity, or horizontal fluxes of water vapour, salinity, energy and other geophysical variables. The diagram is based on <span>a principal component</span> analysis of the two-dimensional structure of the mean squared error matrix between model and observations. This matrix is separated in two parts corresponding to the bias and the relative rotation of the empirical orthogonal functions of the data. We test the performance of this new diagram identifying the differences amongst <span>a</span> reference dataset and different model outputs using examples wind velocities, current, vertically integrated moisture transport and wave energy flux time series. An alternative setup is also <span>proposed</span> with an application to the time-averaged spatial field of surface wind velocity in the Northern and Southern Hemispheres according to different reanalyses and realizations of an ensemble of CMIP5 models. The examples of the use of the Sailor diagram show that it is a tool which helps identifying errors due to the bias or the orientation of the simulated vector time series or fields. An implementation of the algorithm in form of an R package (sailoR) is already publicly available from the CRAN repository, and besides the ability to plot the individual components of the error matrix, functions in the package also allow to easily retrieve the individual components of the mean squared error.</p>

scholarly journals On the Stochastic Restrictedr-kClass Estimator and Stochastic Restrictedr-dClass Estimator in Linear Regression Model

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Jibo Wu
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Mean Squared Error ◽  
Multiple Linear Regression Model ◽  
Error Matrix ◽  
Squared Error ◽  
The Mean ◽  
Linear Restrictions ◽  
Theoretical Results

The stochastic restrictedr-kclass estimator and stochastic restrictedr-dclass estimator are proposed for the vector of parameters in a multiple linear regression model with stochastic linear restrictions. The mean squared error matrix of the proposed estimators is derived and compared, and some properties of the proposed estimators are also discussed. Finally, a numerical example is given to show some of the theoretical results.

scholarly journals The change in estimate method for selecting confounders: A simulation study

2021 ◽  
pp. 096228022110342
Author(s):  
Denis Talbot ◽  
Awa Diop ◽  
Mathilde Lavigne-Robichaud ◽  
Chantal Brisson
Keyword(s):  
Confidence Intervals ◽  
Simulation Study ◽  
Mean Squared Error ◽  
Real Data ◽  
Significance Test ◽  
Simulation Studies ◽  
Squared Error ◽  
Estimate Method ◽  
The Mean ◽  
Work And Health

Background The change in estimate is a popular approach for selecting confounders in epidemiology. It is recommended in epidemiologic textbooks and articles over significance test of coefficients, but concerns have been raised concerning its validity. Few simulation studies have been conducted to investigate its performance. Methods An extensive simulation study was realized to compare different implementations of the change in estimate method. The implementations were also compared when estimating the association of body mass index with diastolic blood pressure in the PROspective Québec Study on Work and Health. Results All methods were susceptible to introduce important bias and to produce confidence intervals that included the true effect much less often than expected in at least some scenarios. Overall mixed results were obtained regarding the accuracy of estimators, as measured by the mean squared error. No implementation adequately differentiated confounders from non-confounders. In the real data analysis, none of the implementation decreased the estimated standard error. Conclusion Based on these results, it is questionable whether change in estimate methods are beneficial in general, considering their low ability to improve the precision of estimates without introducing bias and inability to yield valid confidence intervals or to identify true confounders.

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