scholarly journals Estimating Risk and the Mean Squared Error Matrix in Stein Estimation

2002 ◽  
Vol 82 (1) ◽  
pp. 39-64 ◽  
Author(s):  
T. Kubokawa ◽  
M.S. Srivastava
Keyword(s):  
Mean Squared Error ◽  
Error Matrix ◽  
Mean Squared Error Matrix ◽  
Stein Estimation ◽  
Squared Error ◽  
The Mean

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 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.

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 Sailor diagram – A new diagram for the verification of two-dimensional vector data from multiple models

2020 ◽  
Vol 13 (7) ◽  
pp. 3221-3240
Author(s):  
Jon Sáenz ◽  
Sheila Carreno-Madinabeitia ◽  
Ganix Esnaola ◽  
Santos J. González-Rojí ◽  
Gabriel Ibarra-Berastegi ◽  
...  
Keyword(s):  
Time Series ◽  
Mean Squared Error ◽  
Cmip5 Models ◽  
Multiple Models ◽  
Two Dimensional ◽  
Vector Data ◽  
Reference Dataset ◽  
Error Matrix ◽  
Squared Error ◽  
The Mean

Abstract. A new diagram is proposed for the verification of vector quantities generated by multiple models against a set of observations. It has been designed with the objective, as in the Taylor diagram, of providing a visual diagnostic tool which allows an easy comparison of simulations by multiple models against a reference dataset. However, the Sailor diagram extends this ability to two-dimensional quantities such as currents, wind, horizontal fluxes of water vapour and other geophysical variables by adding features which allow us to evaluate directional properties of the data as well. The diagram is based on the analysis of the two-dimensional structure of the mean squared error matrix between model and observations. This matrix is separated in a part corresponding to the bias and the relative rotation of the two orthogonal directions (empirical orthogonal functions; EOFs) which best describe the vector data. Since there is no truncation of the retained EOFs, these orthogonal directions explain the total variability of the original dataset. We test the performance of this new diagram to identify the differences amongst the reference dataset and a series of model outputs by using some synthetic datasets and real-world examples with time series of variables such as wind, current and vertically integrated moisture transport. An alternative setup for spatially varying time-fixed fields is shown in the last examples, in which the spatial average of surface wind in the Northern and Southern Hemisphere according to different reanalyses and realizations from ensembles of CMIP5 models are compared. The Sailor diagrams presented here show that it is a tool which helps in identifying errors due to the bias or the orientation of the simulated vector time series or fields. The R implementation of the diagram presented together with this paper allows us also to easily retrieve the individual diagnostics of the different components of the mean squared error and additional diagnostics which can be presented in tabular form.

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