scholarly journals MSE of the best linear predictor in nonorthogonal models

2007 ◽  
Vol 57 (1) ◽  
Author(s):  
František Štulajter
Keyword(s):  
Time Series ◽  
White Noise ◽  
Mean Squared Error ◽  
Linear Predictor ◽  
Squared Error ◽  
Additive White Noise ◽  
Best Linear Predictor ◽  
The Mean ◽  
Finite Observation ◽  
Noise Models

AbstractThe problem of computing the mean squared error (MSE) of the best linear predictor (BLP) in finite discrete spectrum with an additive white noise models(FDSWNMs) for an observed time series is considered. This is done under the assumption that the corresponding vectors in models for finite observation of this time series are not orthogonal.

Linear Prediction of a True Score From a Direct Estimate and Several Derived Estimates

2007 ◽  
Vol 32 (1) ◽  
pp. 6-23 ◽  
Author(s):  
Shelby J. Haberman ◽  
Jiahe Qian
Keyword(s):  
Linear Prediction ◽  
Mean Squared Error ◽  
Weighted Average ◽  
Statistical Prediction ◽  
True Score ◽  
Direct Estimate ◽  
Linear Predictor ◽  
Squared Error ◽  
Best Linear Predictor ◽  
Prediction Problems

Statistical prediction problems often involve both a direct estimate of a true score and covariates of this true score. Given the criterion of mean squared error, this study determines the best linear predictor of the true score given the direct estimate and the covariates. Results yield an extension of Kelley’s formula for estimation of the true score to cases in which covariates are present. The best linear predictor is a weighted average of the direct estimate and of the linear regression of the direct estimate onto the covariates. The weights depend on the reliability of the direct estimate and on the multiple correlation of the true score with the covariates. One application of the best linear predictor is to use essay features provided by computer analysis and an observed holistic score of an essay provided by a human rater to approximate the true score corresponding to the holistic score.

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 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.

scholarly journals Fuzzy Time Series for Projecting School Enrolment in Malaysia

2021 ◽  
Vol 6 (1) ◽  
pp. 11-21
Author(s):  
Nor Hayati Shafii ◽  
Rohana Alias ◽  
Siti Rohani Shamsuddin ◽  
Diana Sirmayunie Mohd Nasir
Keyword(s):  
Time Series ◽  
Mean Squared Error ◽  
Time Series Model ◽  
Fuzzy Time Series ◽  
Absolute Deviation ◽  
Error Measure ◽  
Squared Error ◽  
Complete Procedure ◽  
The Mean ◽  
Absolute Percent Error

There are a variety of approaches to the problem of predicting educational enrolment.  However, none of them can be used when the historical data are linguistic values.  Fuzzy time series is an efficient and effective tool to deal with such problems. In this paper, the forecast of the enrolment of pre-primary, primary, secondary, and tertiary schools in Malaysia is carried out using fuzzy time series approaches. A fuzzy time series model is developed using historical dataset collected from the United Nations Educational, Scientific, and Cultural Organization (UNESCO) from the year 1981 to 2018.  A complete procedure is proposed which includes: fuzzifying the historical dataset, developing a fuzzy time series model, and calculating and interpreting the outputs. The accuracy of the model are also examined to evaluate how good the developed forecasting model is. It is tested based on the value of the mean squared error (MSE), Mean Absolute Percent Error (MAPE) and Mean Absolute Deviation (MAD).  The lower the value of error measure, the higher the accuracy of the model.  The result shows that fuzzy time series model developed for primary school enrollments is the most accurate with the lowest error measure, with the MSE value being 0.38, MAPE 0.43 and MAD 0.43 respectively.

scholarly journals The Sailor diagram. An extension of Taylor’s diagram to two-dimensional vector data

2019 ◽  
Author(s):  
Jon Sáenz ◽  
Sheila Carreno-Madinabeitia ◽  
Ganix Esnaola ◽  
Santos J. González-Rojí ◽  
Gabriel Ibarra-Berastegi ◽  
...  
Keyword(s):  
Time Series ◽  
Mean Squared Error ◽  
Empirical Orthogonal Functions ◽  
Cmip5 Models ◽  
Spatial Average ◽  
Two Dimensional ◽  
Error Matrix ◽  
Squared Error ◽  
Taylor Diagram ◽  
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 idea of extending the Taylor diagram to two dimensional quantities such as currents, wind, or horizontal fluxes of water vapour, salinity, energy and other geophysical variables. 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 empirical orthogonal functions of the data. We test the performance of this new diagram to identify the differences amongst the reference dataset and the different model outputs by using examples with wind, current, vertically integrated moisture transport and wave energy flux time series. An alternative setup is shown in the last examples, where the spatial average of surface wind in the Northern and Southern Hemispheres according to different reanalyses and realizations of CMIP5 models are compared. The examples of use of the Sailor diagram presented 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 also to easily retrieve the individual diagnostics of the different components of the mean squared error.

Computing trade-offs in robust design: Perspectives of the mean squared error

2011 ◽  
Vol 60 (2) ◽  
pp. 248-255 ◽  
Author(s):  
Sangmun Shin ◽  
Funda Samanlioglu ◽  
Byung Rae Cho ◽  
Margaret M. Wiecek
Keyword(s):  
Robust Design ◽  
Mean Squared Error ◽  
Squared Error ◽  
Trade Offs ◽  
The Mean

scholarly journals Day-Ahead Forecasting of Hourly Photovoltaic Power Based on Robust Multilayer Perception

2018 ◽  
Vol 10 (12) ◽  
pp. 4863 ◽  
Author(s):  
Chao Huang ◽  
Longpeng Cao ◽  
Nanxin Peng ◽  
Sijia Li ◽  
Jing Zhang ◽  
...  
Keyword(s):  
Power Plants ◽  
Mean Squared Error ◽  
Absolute Error ◽  
Multilayer Perception ◽  
Squared Error ◽  
The Mean ◽  
Effectiveness And Efficiency ◽  
Mlp Network ◽  
Grid Operation ◽  
Better Than

Photovoltaic (PV) modules convert renewable and sustainable solar energy into electricity. However, the uncertainty of PV power production brings challenges for the grid operation. To facilitate the management and scheduling of PV power plants, forecasting is an essential technique. In this paper, a robust multilayer perception (MLP) neural network was developed for day-ahead forecasting of hourly PV power. A generic MLP is usually trained by minimizing the mean squared loss. The mean squared error is sensitive to a few particularly large errors that can lead to a poor estimator. To tackle the problem, the pseudo-Huber loss function, which combines the best properties of squared loss and absolute loss, was adopted in this paper. The effectiveness and efficiency of the proposed method was verified by benchmarking against a generic MLP network with real PV data. Numerical experiments illustrated that the proposed method performed better than the generic MLP network in terms of root mean squared error (RMSE) and mean absolute error (MAE).

scholarly journals On double stage minimax-shrinkage estimator for generalized Rayleigh model

2016 ◽  
Vol 5 (1) ◽  
pp. 39 ◽  
Author(s):  
Abbas Najim Salman ◽  
Maymona Ameen
Keyword(s):  
Sample Size ◽  
Shape Parameter ◽  
Mean Squared Error ◽  
Scale Parameter ◽  
Rayleigh Distribution ◽  
Shrinkage Estimator ◽  
Squared Error ◽  
Expected Sample Size ◽  
Generalized Rayleigh Distribution ◽  
The Mean

<p>This paper is concerned with minimax shrinkage estimator using double stage shrinkage technique for lowering the mean squared error, intended for estimate the shape parameter (a) of Generalized Rayleigh distribution in a region (R) around available prior knowledge (a<sub>0</sub>) about the actual value (a) as initial estimate in case when the scale parameter (l) is known .</p><p>In situation where the experimentations are time consuming or very costly, a double stage procedure can be used to reduce the expected sample size needed to obtain the estimator.</p><p>The proposed estimator is shown to have smaller mean squared error for certain choice of the shrinkage weight factor y(<strong>×</strong>) and suitable region R.</p><p>Expressions for Bias, Mean squared error (MSE), Expected sample size [E (n/a, R)], Expected sample size proportion [E(n/a,R)/n], probability for avoiding the second sample and percentage of overall sample saved  for the proposed estimator are derived.</p><p>Numerical results and conclusions for the expressions mentioned above were displayed when the consider estimator are testimator of level of significanceD.</p><p>Comparisons with the minimax estimator and with the most recent studies were made to shown the effectiveness of the proposed estimator.</p>

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