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Journal articles on the topic 'Mean square errors'

Author: Grafiati

Published: 4 June 2021

Last updated: 21 February 2023

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1

Hodson, Timothy O. "Root-mean-square error (RMSE) or mean absolute error (MAE): when to use them or not." Geoscientific Model Development 15, no. 14 (July 19, 2022): 5481–87. http://dx.doi.org/10.5194/gmd-15-5481-2022.

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Abstract. The root-mean-squared error (RMSE) and mean absolute error (MAE) are widely used metrics for evaluating models. Yet, there remains enduring confusion over their use, such that a standard practice is to present both, leaving it to the reader to decide which is more relevant. In a recent reprise to the 200-year debate over their use, Willmott and Matsuura (2005) and Chai and Draxler (2014) give arguments for favoring one metric or the other. However, this comparison can present a false dichotomy. Neither metric is inherently better: RMSE is optimal for normal (Gaussian) errors, and MAE is optimal for Laplacian errors. When errors deviate from these distributions, other metrics are superior.

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2

Robeson, Scott M., and Cort J. Willmott. "Decomposition of the mean absolute error (MAE) into systematic and unsystematic components." PLOS ONE 18, no. 2 (February 17, 2023): e0279774. http://dx.doi.org/10.1371/journal.pone.0279774.

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When evaluating the performance of quantitative models, dimensioned errors often are characterized by sums-of-squares measures such as the mean squared error (MSE) or its square root, the root mean squared error (RMSE). In terms of quantifying average error, however, absolute-value-based measures such as the mean absolute error (MAE) are more interpretable than MSE or RMSE. Part of that historical preference for sums-of-squares measures is that they are mathematically amenable to decomposition and one can then form ratios, such as those based on separating MSE into its systematic and unsystematic components. Here, we develop and illustrate a decomposition of MAE into three useful submeasures: (1) bias error, (2) proportionality error, and (3) unsystematic error. This three-part decomposition of MAE is preferable to comparable decompositions of MSE because it provides more straightforward information on the nature of the model-error distribution. We illustrate the properties of our new three-part decomposition using a long-term reconstruction of streamflow for the Upper Colorado River.

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3

Kishimoto, K., K. Onaga, and E. Nakamae. "Theoretical assessment of mean square errors of antialiasing filters." Computer Vision, Graphics, and Image Processing 35, no. 2 (August 1986): 277. http://dx.doi.org/10.1016/0734-189x(86)90043-5.

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4

Kishimoto, K., K. Onaga, and E. Nakamae. "Theoretical assessments of mean square errors of antialiasing filters." Computer Vision, Graphics, and Image Processing 37, no. 3 (March 1987): 428–37. http://dx.doi.org/10.1016/0734-189x(87)90047-8.

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5

Clements, Michael P., and David F. Hendry. "On the limitations of comparing mean square forecast errors." Journal of Forecasting 12, no. 8 (December 1993): 617–37. http://dx.doi.org/10.1002/for.3980120802.

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6

Ogasawara, Haruhiko. "Optimal Information Criteria Minimizing Their Asymptotic Mean Square Errors." Sankhya B 78, no. 1 (March 10, 2016): 152–82. http://dx.doi.org/10.1007/s13571-016-0115-9.

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7

Jadhav, Smita, and Dipika Jaspal. "Adsorptive eradication of tartrazine from aqueous solutions onto doped polyaniline." Journal of the Serbian Chemical Society 85, no. 2 (2020): 251–63. http://dx.doi.org/10.2298/jsc190705116j.

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A potential polymeric adsorbent, doped polyaniline (PANI) has been investigated for the eradication of the hazardous dye tartrazine from textile effluent. During the adsorption process, the influence of the acidic character of the adsorbate, pH, dose of the adsorbent, dye concentration and time of contact between the adsorbent and adsorbate were evaluated. The outcomes attained from batch experiments were applied to the Langmuir and the Freundlich isothermal models. Different error analysis techniques, such as mean square error, root mean square error, the Chi-square test (?2), sum of absolute errors and sum of squared errors, were determined for the doped polyaniline?tartrazine system. The Langmuir isotherm was established as the best-fit isothermal model, with minimum errors and high regression values. About 90?97 % removal was achieved in the first 70 min. A positive enthalpy value implied the adsorption process was endothermic. The energy of activation for the dye adsorbent system was found to be 28.9 kJ mol-1, which is in line with physisorption.

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8

Nakonechnyi, Alexander, Grigoriy Kudin, Taras Zinko, and Petr Zinko. "MINIMAX ROOT–MEAN–SQUARE ESTIMATES OF MATRIX PARAMETERS IN LINEAR REGRESSION PROBLEMS UNDER UNCERTAINTY." Journal of Automation and Information sciences 4 (July 1, 2021): 28–37. http://dx.doi.org/10.34229/1028-0979-2021-4-3.

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The issues of parameter estimation in linear regression problems with random matrix coefficients were researched. Given that random linear functions are observed from unknown matrices with random errors that have unknown correlation matrices, the problems of guaranteed mean square estimation of linear functions of matrices were investigated. The estimates of the upper and lower guaranteed standard errors of linear estimates of observations of linear functions of matrices were obtained in the case when the sets are found, for which the unknown matrices and correlation matrices of observation errors are known. It was proved that for some partial cases such estimates are accurate. Assuming that the sets are bounded, convex and closed, more accurate two-sided estimates have been gained for guaranteed errors. The conditions when the guaranteed mean squared errors approach zero as the number of observations increases were found. The necessary and sufficient conditions for the unbiasedness of linear estimates of linear functions of matrices were provided. The notion of quasi-optimal estimates for linear functions of matrices was introduced, and it was proved that in the class of unbiased estimates, quasi-optimal estimates exist and are unique. For such estimates, the conditions of convergence to zero of the guaranteed mean-square errors were obtained. Also, for linear estimates of unknown matrices, the concept of quasi-minimax estimates was introduced and it was confirmed that they are unbiased. For special sets, which include an unknown matrix and correlation matrices of observation errors, such estimates were expressed through the solution of linear operator equations in a finite-dimensional space. For quasi-minimax estimates under certain assumptions, the form of the guaranteed mean squared error of the unknown matrix was found. It was shown that such errors are limited by the sum of traces of the known matrices. An example of finding a minimax unbiased linear estimation was given for a special type of random matrices that are included in the observation equation.

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9

Anh, Nguyen Dong, and Nguyen Minh Triet. "A FULL DUAL MEAN SQUARE ERROR CRITERION FOR THE EQUIVALENT LINEARIZATION." Vietnam Journal of Science and Technology 54, no. 4 (August 18, 2016): 557. http://dx.doi.org/10.15625/0866-708x/54/4/8103.

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Among approximate methods, the method of equivalent linearization proposed by N. Krylov and N. Bogoliubov and extended by Caughey has remained an effective tool for both deterministic and stochastic problems. The idea of the method is based on the replacement of a nonlinear oscillator by a linear one under the same excitation. The standard way of implementing this method is that the coefficients of linearization are to be found from a criterion of equivalence. When the difference between the nonlinear function and equivalent linear one is significant the replacement leads to unaccepted errors. In order to reduce the errors one may apply the dual approach. One of significant advantages of the dual conception is its consideration of two different aspects of a problem in question allowing the investigation to be more appropriate. In this paper a special case of the weighted full dual mean square error criterion is introduced and investigated in detail. Numerical results are carried out to show that this special full dual mean square error criterion can give more accurate approximate solutions for both deterministic and random nonlinear systems.

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10

Ogasawara, Haruhiko. "Predictive estimation of variances and covariances using mean square errors." Proceedings of the Annual Convention of the Japanese Psychological Association 83 (September 11, 2019): 1A—039–1A—039. http://dx.doi.org/10.4992/pacjpa.83.0_1a-039.

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11

Киричук, Юрій Володимирович. "Mean-square errors of object positioning in rectangular coordinate system." Technology audit and production reserves 1, no. 4(15) (February 6, 2014): 21. http://dx.doi.org/10.15587/2312-8372.2014.21694.

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12

Salmon, Thomas O., and Corina van de Pol. "Normal-eye Zernike coefficients and root-mean-square wavefront errors." Journal of Cataract & Refractive Surgery 32, no. 12 (December 2006): 2064–74. http://dx.doi.org/10.1016/j.jcrs.2006.07.022.

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13

Baillie, Richard T., and Francis X. Diebold. "On the limitations of comparing mean square forecast errors: Commentary." Journal of Forecasting 12, no. 8 (December 1993): 639–41. http://dx.doi.org/10.1002/for.3980120803.

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14

Diebold, Francis X. "On the limitations of comparing mean square forecast errors: Comment." Journal of Forecasting 12, no. 8 (December 1993): 641–42. http://dx.doi.org/10.1002/for.3980120804.

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15

Granger, Clive W. J. "On the limitations of comparing mean square forecast errors: Comment." Journal of Forecasting 12, no. 8 (December 1993): 651–52. http://dx.doi.org/10.1002/for.3980120807.

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16

Philip Howrey, E. "On the limitations of comparing mean square forecast errors: Comment." Journal of Forecasting 12, no. 8 (December 1993): 652–54. http://dx.doi.org/10.1002/for.3980120808.

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17

McNees, Stephen K. "On the limitations of comparing mean square forecast errors: Comment." Journal of Forecasting 12, no. 8 (December 1993): 654–56. http://dx.doi.org/10.1002/for.3980120809.

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18

Meese, Richard A. "On the limitations of comparing mean square forecast errors: Comment." Journal of Forecasting 12, no. 8 (December 1993): 656–58. http://dx.doi.org/10.1002/for.3980120810.

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19

Newbold, Paul. "On the limitations of comparing mean square forecast errors: Comment." Journal of Forecasting 12, no. 8 (December 1993): 658–60. http://dx.doi.org/10.1002/for.3980120811.

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20

Schmidt, Peter. "On the limitations of comparing mean square forecast errors: Comment." Journal of Forecasting 12, no. 8 (December 1993): 660–62. http://dx.doi.org/10.1002/for.3980120812.

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21

Wallis, Kenneth F. "On the limitations of comparing mean square forecast errors: Comment." Journal of Forecasting 12, no. 8 (December 1993): 663–66. http://dx.doi.org/10.1002/for.3980120813.

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22

West, Kenneth D. "On the limitations of comparing mean square forecast errors: Comment." Journal of Forecasting 12, no. 8 (December 1993): 666–67. http://dx.doi.org/10.1002/for.3980120814.

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23

Octavia, Ranti Wilda Nur, and Umi Chotijah. "Implementasi Metode Least Square Untuk Prediksi Penjualan Kue Donat dan Bomboloni." Jutisi : Jurnal Ilmiah Teknik Informatika dan Sistem Informasi 11, no. 1 (April 8, 2022): 251. http://dx.doi.org/10.35889/jutisi.v11i1.802.

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<p><strong>Abstrak.</strong> Prediksi Jumlah permintaan kue donat dan bomboloni oleh pelanggan (konsumen) Toko <em>Milly Donuts</em> selama ini tidak akurat, dimana jumlah produksi tidak sesuai dengan jumlah permintaan konsumen. Penelitian ini bertujuan mengimplementasikan Metode <em>Least Square</em> untuk melakukan <em>forecast</em> (prediksi) dalam penjualan. Metode <em>Least Square</em> merupakan salah satu teknik dalam menyusun <em>forecast</em> penjualan dengan meminimumkan fungsi kriteria jumlah kuadrat kesalahan prediksi serta menggunakan <em>Mean Squad Error</em> (MSE), <em>Mean Absolute Deviation</em> (MAD) dan <em>Mean Absolute Percentage Error</em> (MAPE) untuk mengetahui tingkat kesalahan dalam metode <em>least square</em>. Prediksi menggunakan metode <em>Trend Least Square, </em>dimana nilai peramalan yang didapatkan diharapkan sesuai data aktual. Data yang dipakai dalam penelitian ini merupakan pencatatan penjualan kue donat dan bomboloni pada bulan Januari 2021 hinggai bulan Desember 2021. Hasil penelitian memperoleh <em>forecast</em> penjualan untuk bulan Januari hingga Maret 2022 sebanyak 1550,1579,1608 dengan kesalahan sebesar 0,34 pada MAD, 1,707 pada MSE dan 0,03602% pada MAPE.</p><p><strong>Kata kunci</strong><strong><em>:</em></strong><em> </em>Prediksi<em>; Least Square; Mean Squad Error;</em> <em>Mean Absolute Deviation;</em> <em>Mean Absolute Percentage Error</em><strong></strong></p><p align="center"><em> </em></p><p><em><strong>Abstract</strong>. Prediction of requests amount for donuts and bomboloni by customers (consumers) of Milly Donuts Shop so far is not accurate, where the amount of production does not match the number of consumer requests. This study aims to implement the Least Square Method to forecast (prediction) in sales. The Least Square method is one of the techniques in preparing sales forecasts by minimizing the criterion function for the number of squares of prediction errors and using Mean Squad Error (MSE), Mean Absolute Deviation (MAD) and Mean Absolute Percentage Error (MAPE) to determine the error rate in the least squares method. Prediction using the Trend Least Square method, where the forecast value obtained is expected to match the actual data. The data used in this study is the recording of sales of donuts and bomboloni in January 2021 to December 2021. The results of the study obtained sales forecasts for January to March 2022 as many as 1550,1579,1608 with errors of 0.34 in MAD, 1.707 in MSE and 0.03602% on MAPE.</em></p><p><strong><em>Keywords:</em></strong><em> Prediction; Least Square; Mean Squad Errors; Mean Absolute Deviation; Mean Absolute Percentage Error</em></p>

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Pereira, Janser Moura, Joel Augusto Muniz, and Carlos Alberto Silva. "Nonlinear models to predict nitrogen mineralization in an Oxisol." Scientia Agricola 62, no. 4 (August 2005): 395–400. http://dx.doi.org/10.1590/s0103-90162005000400014.

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This work was carried out to evaluate the statistical properties of eight nonlinear models used to predict nitrogen mineralization in soils of the Southern Minas Gerais State, Brazil. The parameter estimations for nonlinear models with and without structure of autoregressive errors was made by the least squares method. First, a structure of second order autoregressive errors, AR(2) was considered for all nonlinear models and then the significance of the autocorrelation parameters was verified. Among the models, the Juma presented an autocorrelation of second order, and the model of Broadbent presented one of first order. In summary, these models presented significant autocorrelation parameters. To estimate the parameters of nonlinear models, the SAS procedure MODEL was used (SAS). The comparison of the models was made by measuring the fitted parameters: adjusted R-square, mean square error and mean predicted error. The Juma model with AR(2) best fitted for nitrogen mineralization without liming, followed by Cabrera, Stanford & Smith without autoregressive errors, for both with and without soil acidity correction.

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25

Xiao-Ping, Zheng, Chu Yuan-Liang, Zhao Wei, Zhang Han-Yi, and Guo Yi-Li. "Measurement of Root-Mean-Square Phase Errors in Arrayed Waveguide Gratings." Chinese Physics Letters 21, no. 2 (February 2004): 335–36. http://dx.doi.org/10.1088/0256-307x/21/2/034.

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26

Engle, Robert F. "On the limitations of com??aring mean square forecast errors: Comment." Journal of Forecasting 12, no. 8 (December 1993): 642–44. http://dx.doi.org/10.1002/for.3980120805.

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Clements, Michael P., and David F. Hendry. "On the limitations of comparing mean square forecast errors: A reply." Journal of Forecasting 12, no. 8 (December 1993): 669–76. http://dx.doi.org/10.1002/for.3980120815.

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MANI, RAJA, DR TALWALKAR, SATHY NAIR, and DR SIKKA. "Optimum grid length for analysis of wind field with respect to the existing network of upper air observing stations over India and its neighbourhood." MAUSAM 37, no. 3 (July 1, 1986): 289–92. http://dx.doi.org/10.54302/mausam.v37i3.2372.

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The optimum grid length for the analysis of wind field with respect to the existing network of upper air observing stations over India and the neighbourhood is determined. This is done in the following way. Analyses of wind field at 700 mb level for 31 days (July 1979) for six different grid lengths were made by a standard objective method and the root mean square errors of analysis were computed. The grid length for which the average root mean square error has been minimum, was determined. The dependence of root mean square errors on the number of observations used as input has also been examined.

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Prasetyowati, Sri Arttini Dwi, Munaf Ismail, and Badieah Badieah. "Implementation of Least Mean Square Adaptive Algorithm on Covid-19 Prediction." JUITA: Jurnal Informatika 10, no. 1 (May 27, 2022): 139. http://dx.doi.org/10.30595/juita.v10i1.11963.

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This study used Corona Virus Disease-19 (Covid-19) data in Indonesia from June to August 2021, consisting of data on people who were infected or positive Covid-19, recovered from Covid-19, and passed away from Covid-19. The data were processed using the adaptive LMS algorithm directly without pre-processing cause calculation errors, because covid-19 data was not balanced. Z-score and min-max normalization were chosen as pre-processing methods. After that, the prediction process can be carried out using the LMS adaptive method. The analysis was done by observing the error prediction that occurred every month per case. The results showed that data pre-processing using min-max normalization was better than with Z-score normalization because the error prediction for pre-processing using min-max and z-score were 18% and 47%, respectively.

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Kassabian, Nazelie, Letizia Lo Presti, and Francesco Rispoli. "Augmented GNSS Differential Corrections Minimum Mean Square Error Estimation Sensitivity to Spatial Correlation Modeling Errors." Sensors 14, no. 6 (June 11, 2014): 10258–72. http://dx.doi.org/10.3390/s140610258.

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31

Simin, Timothy. "The Poor Predictive Performance of Asset Pricing Models." Journal of Financial and Quantitative Analysis 43, no. 2 (June 2008): 355–80. http://dx.doi.org/10.1017/s0022109000003550.

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AbstractThis paper examines time-series forecast errors of expected returns from conditional and unconditional asset pricing models for portfolio and individual firm equity returns. A new result that increases predictive precision concerning model specification and forecasting is introduced. Conditional versions of the models generally produce higher mean squared errors than unconditional versions for step ahead prediction. This holds for individual firm data when the instruments are firm specific. Mean square forecast error decompositions indicate that the asset pricing models produce relatively unbiased predictions, but the variance is severe enough to ruin the step ahead predictive ability beyond that of a constant benchmark.

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Olasunkanmi Muili, Jamiu, Ahmed Audu, and Ibrahim Yunusa Adamu. "On The Efficiency of Ratio Estimators of Finite Population Mean Using Auxiliary Information." Oriental Journal of Physical Sciences 6, no. 1-2 (February 28, 2022): 07–14. http://dx.doi.org/10.13005/ojps06.01-02.03.

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Ratio estimation is a technique that usages available auxiliary information which is certainly correlated with study variables. In this study, a class of ratio-type estimators of finite population means has been anticipated to solve delinquent of estimation of the population mean. Properties of anticipated estimators namely Bias & Mean Square Error were acquired up to the first order of approximation & the condition for their efficiency over some existing estimators was also established. The results show that anticipated estimators are enhanced & proficient (minimum mean square errors) than other estimators with the highest precision.

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SÖKÜT AÇAR, Tuğba. "Kibria-Lukman Estimator for General Linear Regression Model with AR(2) Errors: A Comparative Study with Monte Carlo Simulation." Journal of New Theory, no. 41 (December 31, 2022): 1–17. http://dx.doi.org/10.53570/jnt.1139885.

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The sensitivity of the least-squares estimation in a regression model is impacted by multicollinearity and autocorrelation problems. To deal with the multicollinearity, Ridge, Liu, and Ridge-type biased estimators have been presented in the statistical literature. The recently proposed Kibria-Lukman estimator is one of the Ridge-type estimators. The literature has compared the Kibria-Lukman estimator with the others using the mean square error criterion for the linear regression model. It was achieved in a study conducted on the Kibria-Lukman estimator's performance under the first-order autoregressive erroneous autocorrelation. When there is an autocorrelation problem with the second-order, evaluating the performance of the Kibria-Lukman estimator according to the mean square error criterion makes this paper original. The scalar mean square error of the Kibria-Lukman estimator under the second-order autoregressive error structure was evaluated using a Monte Carlo simulation and two real examples, and compared with the Generalized Least-squares, Ridge, and Liu estimators. The findings revealed that when the variance of the model was small, the mean square error of the Kibria-Lukman estimator gave very close values with the popular biased estimators. As the model variance grew, Kibria-Lukman did not give fairly similar values with popular biased estimators as in the model with small variance. However, according to the mean square error criterion the Kibria-Lukman estimator outperformed the Generalized Least-Squares estimator in all possible cases.

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Yang, Xiaosong, Timothy DelSole, and Hua-Lu Pan. "Empirical Correction of the NCEP Global Forecast System." Monthly Weather Review 136, no. 12 (December 1, 2008): 5224–33. http://dx.doi.org/10.1175/2008mwr2527.1.

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Abstract This paper examines the extent to which an empirical correction method can improve forecasts of the National Centers for Environmental Prediction (NCEP) operational Global Forecast System. The empirical correction is based on adding a forcing term to the prognostic equations equal to the negative of the climatological tendency errors. The tendency errors are estimated by a least squares method using 6-, 12-, 18-, and 24-h forecast errors. Tests on independent verification data show that the empirical correction significantly reduces temperature biases nearly everywhere at all lead times up to at least 5 days but does not significantly reduce biases in forecast winds and humidity. Decomposing mean-square error into bias and random components reveals that the reduction in total mean-square error arises solely from reduction in bias. Interestingly, the empirical correction increases the random error slightly, but this increase is argued to be an artifact of the change in variance in the forecasts. The empirical correction also is found to reduce the bias more than traditional “after the fact” corrections. The latter result might be a consequence of the very different sample sizes available for estimation, but this difference in sample size is unavoidable in operational situations in which limited calibration data are available for a given forecast model.

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Ding, Li Bo, He Zhang, and Jian Jing Liu. "Error Compensation of 3-Axis Magnetoresistive Magnetometer." Applied Mechanics and Materials 130-134 (October 2011): 1391–95. http://dx.doi.org/10.4028/www.scientific.net/amm.130-134.1391.

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To eliminate errors of 3-axis magnetoresistive magnetometer, according to its offset errors, sensitivity errors and non-orthogonal errors which specialty was considered, an error compensation model of magnetoresistive magnetometer was established. And the calculation method of the error compensation model, which did not need accelerometers, was proposed to correct the magnetometer errors. The results show the algorithm of error compensation model decrease the root mean square error of the magnetometer from 413nT to 82nT. Thus the 3-axis magnetoresistive magnetometer could fast and accurately measure the geomagnetic field.

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Ericsson, Neil R. "On the limitations of comparing mean square forecast errors: Clarifications and extensions." Journal of Forecasting 12, no. 8 (December 1993): 644–51. http://dx.doi.org/10.1002/for.3980120806.

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Zhang, Junhua, Yuping Hu, and Sanying Feng. "Self-Consistent Density Estimation in the Presence of Errors-in-Variables." Abstract and Applied Analysis 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/958702.

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This paper considers the estimation of the common probability density of independent and identically distributed variables observed with additive measurement errors. The self-consistent estimator of the density function is constructed when the error distribution is known, and a modification of the self-consistent estimation is proposed when the error distribution is unknown. The consistency properties of the proposed estimators and the upper bounds of the mean square error and mean integrated square error are investigated under some suitable conditions. Simulation studies are carried out to assess the performance of our proposed method and compare with the usual deconvolution kernel method. Two real datasets are analyzed for further illustration.

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Tcheou, Michel Pompeu, Lisandro Lovisolo, Alexandre Ribeiro Freitas, and Sin Chan Chou. "Reducing Forecast Errors of a Regional Climate Model Using Adaptive Filters." Applied Sciences 11, no. 17 (August 29, 2021): 8001. http://dx.doi.org/10.3390/app11178001.

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In this work, the use of adaptive filters for reducing forecast errors produced by a Regional Climate Model (RCM) is investigated. Seasonal forecasts are compared against the reanalysis data provided by the National Centers for Environmental Prediction. The reanalysis is used to train adaptive filters based on the Recursive Least Squares algorithm in order to reduce the forecast error. The K-means unsupervised learning algorithm is used to obtain the number of filters to employ from the climate variables. The proposed approach is applied to some climate variables such as the meridional wind, zonal wind, and the geopotential height. The forecast is produced by the Eta RCM at 40-km resolution in a domain covering most of Brazil. Results show that the proposed approach is capable of reducing the forecast errors, according to evaluation metrics such as normalized mean square error, maximum absolute error, and maximum normalized absolute error, thus improving the seasonal climate forecasts.

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ناصر, جنان عباس. "Comparison Bayes Estimators of Reliability in the Exponential Distribution." Journal of Economics and Administrative Sciences 24, no. 104 (October 23, 2018): 1. http://dx.doi.org/10.33095/jeas.v24i104.99.

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Abstract We produced a study in Estimation for Reliability of the Exponential distribution based on the Bayesian approach. These estimates are derived using Bayesian approaches. In the Bayesian approach, the parameter of the Exponential distribution is assumed to be random variable .we derived bayes estimators of reliability under four types when the prior distribution for the scale parameter of the Exponential distribution is: Inverse Chi-square distribution, Inverted Gamma distribution, improper distribution, Non-informative distribution. And estimators for Reliability is obtained using the well known squared error loss function and weighted squared errors loss function. We used simulation technique, to compare the resultant estimators in terms of their mean squared errors (MSE), mean weighted squared errors (MWSE).Several cases assumed for the parameter of the exponential distribution for data generating, of different samples sizes (small, medium, and large). The results were obtained by using simulation technique, Programs written using MATLAB-R2008a program were used. In general, Simulation results shown that the resultant estimators in terms of their mean squared errors (MSE) is better than the resultant estimators in terms of their mean weighted squared errors (MWSE).According to the our criteria is the best estimator that gives the smallest value of MSE or MWSE . For example bayes estimation is the best when the prior distribution for the scale parameter is improper and Non-informative distributions according to the smallest value of MSE comparative to the values of MWSE for all samples sizes at some of true value of t and .

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ERBAYRAM, Tenzile, Ümmügülsüm YILDIRIM, and Yunus AKDOĞAN. "A new Lifetime Distribution Based on the Transmuted First Two Lower Records." Cumhuriyet Science Journal 43, no. 3 (September 30, 2022): 534–42. http://dx.doi.org/10.17776/csj.1094289.

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This article introduces a new lifetime distribution by merging the first two lower records based on exponential distribution and discusses the different features of the distribution. Statistical inferences about the distribution parameters are discussed with three estimation methods, namely maximum likelihood, least squares, and weighted least squares. Monte Carlo simulation study is performed to evaluate of these estimators based on mean square errors estimation, mean absolute deviation, and mean relative errors of estimation for a sample of different sizes. A distribution simulation analysis based on real data is provided to demonstrate the adaptability of the proposed model.

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Lee, Stephen Man Sing. "Optimal choice between parametric and non-parametric bootstrap estimates." Mathematical Proceedings of the Cambridge Philosophical Society 115, no. 2 (March 1994): 335–63. http://dx.doi.org/10.1017/s0305004100072121.

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AbstractA parametric bootstrap estimate (PB) may be more accurate than its non-parametric version (NB) if the parametric model upon which it is based is, at least approximately, correct. Construction of an optimal estimator based on both PB and NB is pursued with the aim of minimizing the mean squared error. Our approach is to pick an empirical estimate of the optimal tuning parameter ε∈[0, 1] which minimizes the mean square error of εNB+(1−ε) PB. The resulting hybrid estimator is shown to be more reliable than either PB or NB uniformly over a rich class of distributions. Theoretical asymptotic results show that the asymptotic error of this hybrid estimator is quite close in distribution to the smaller of the errors of PB and NB. All these errors typically have the same convergence rate of order . A particular example is also presented to illustrate the fact that this hybrid estimate can indeed be strictly better than either of the pure bootstrap estimates in terms of minimizing mean squared error. Two simulation studies were conducted to verify the theoretical results and demonstrate the good practical performance of the hybrid method.

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Alam, S. M. Mahfuz, and Mohd Hasan Ali. "Equation Based New Methods for Residential Load Forecasting." Energies 13, no. 23 (December 2, 2020): 6378. http://dx.doi.org/10.3390/en13236378.

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This work proposes two non-linear and one linear equation-based system for residential load forecasting considering heating degree days, cooling degree days, occupancy, and day type, which are applicable to any residential building with small sets of smart meter data. The coefficients of the proposed nonlinear and linear equations are tuned by particle swarm optimization (PSO) and the multiple linear regression method, respectively. For the purpose of comparison, a subtractive clustering based adaptive neuro fuzzy inference system (ANFIS), random forests, gradient boosting trees, and long-term short memory neural network, conventional and modified support vector regression methods were considered. Simulations have been performed in MATLAB environment, and all the methods were tested with randomly chosen 30 days data of a residential building in Memphis City for energy consumption prediction. The absolute average error, root mean square error, and mean average percentage errors are tabulated and considered as performance indices. The efficacy of the proposed systems for residential load forecasting over the other systems have been validated by both simulation results and performance indices, which indicate that the proposed equation-based systems have the lowest absolute average errors, root mean square errors, and mean average percentage errors compared to the other methods. In addition, the proposed systems can be easily practically implemented.

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Walsh, John E., William L. Chapman, Vladimir Romanovsky, Jens H. Christensen, and Martin Stendel. "Global Climate Model Performance over Alaska and Greenland." Journal of Climate 21, no. 23 (December 1, 2008): 6156–74. http://dx.doi.org/10.1175/2008jcli2163.1.

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Abstract The performance of a set of 15 global climate models used in the Coupled Model Intercomparison Project is evaluated for Alaska and Greenland, and compared with the performance over broader pan-Arctic and Northern Hemisphere extratropical domains. Root-mean-square errors relative to the 1958–2000 climatology of the 40-yr ECMWF Re-Analysis (ERA-40) are summed over the seasonal cycles of three variables: surface air temperature, precipitation, and sea level pressure. The specific models that perform best over the larger domains tend to be the ones that perform best over Alaska and Greenland. The rankings of the models are largely unchanged when the bias of each model’s climatological annual mean is removed prior to the error calculation for the individual models. The annual mean biases typically account for about half of the models’ root-mean-square errors. However, the root-mean-square errors of the models are generally much larger than the biases of the composite output, indicating that the systematic errors differ considerably among the models. There is a tendency for the models with smaller errors to simulate a larger greenhouse warming over the Arctic, as well as larger increases of Arctic precipitation and decreases of Arctic sea level pressure, when greenhouse gas concentrations are increased. Because several models have substantially smaller systematic errors than the other models, the differences in greenhouse projections imply that the choice of a subset of models may offer a viable approach to narrowing the uncertainty and obtaining more robust estimates of future climate change in regions such as Alaska, Greenland, and the broader Arctic.

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Zhang, Tao, Baolin Li, Jinfeng Wang, Maogui Hu, and Lili Xu. "Estimation of Areal Mean Rainfall in Remote Areas Using B-SHADE Model." Advances in Meteorology 2016 (2016): 1–13. http://dx.doi.org/10.1155/2016/7643753.

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This study presented a method to estimate areal mean rainfall (AMR) using a Biased Sentinel Hospital Based Area Disease Estimation (B-SHADE) model, together with biased rain gauge observations and Tropical Rainfall Measuring Mission (TRMM) data, for remote areas with a sparse and uneven distribution of rain gauges. Based on the B-SHADE model, the best linear unbiased estimation of AMR could be obtained. A case study was conducted for the Three-River Headwaters region in the Tibetan Plateau of China, and its performance was compared with traditional methods. The results indicated that B-SHADE obtained the least estimation biases, with a mean error and root mean square error of −0.63 and 3.48 mm, respectively. For the traditional methods including arithmetic average, Thiessen polygon, and ordinary kriging, the mean errors were 7.11, −1.43, and 2.89 mm, which were up to 1027.1%, 127.0%, and 358.3%, respectively, greater than for the B-SHADE model. The root mean square errors were 10.31, 4.02, and 6.27 mm, which were up to 196.1%, 15.5%, and 80.0%, respectively, higher than for the B-SHADE model. The proposed technique can be used to extend the AMR record to the presatellite observation period, when only the gauge data are available.

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Dimitriadou, Stavroula, and Konstantinos G. Nikolakopoulos. "Development of the Statistical Errors Raster Toolbox with Six Automated Models for Raster Analysis in GIS Environments." Remote Sensing 14, no. 21 (October 29, 2022): 5446. http://dx.doi.org/10.3390/rs14215446.

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The Statistical Errors Raster Toolbox includes models of the most popular error metrics in the interdisciplinary literature, namely, root mean square error (RMSE), normalized root mean square error (NRMSE), mean bias error (MBE), normalized mean bias error (NMBE), mean absolute error (MAE) and normalized mean absolute error (NMAE), for computing the areal errors of any raster file in .tiff format as compared with a reference raster file. The models are applicable to any size of raster files, no matter if no-data pixels are included. The only prerequisites are that the two raster files share the same units, cell size, and projection system. The novelty lies in the fact that, to date, there is no such application in ArcGIS Pro 3/ArcMap 10.8. Therefore, users who work with raster files require external software, plus the relevant expertise. An application on the reference evapotranspiration (ETo) of Peloponnese peninsula (Greece) is presented. MODIS ET products and ETo raster files for empirical methods are employed. The results of the models (for 20,440 valid values) are compared to the results of external software (for 1000 random points). Considering that the different sample sizes can lead to different accuracies and the inhomogeneity of the area, it is obvious that the results are almost identical.

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Querino, Carlos Alexandre Santos, Marcelo Sacardi Biudes, Nadja Gomes Machado, Juliane Kayse Albuquerque da Silva Querino, Marcos Antônio Lima Moura, and Péricles Vale Alves. "Modelling parametrization to estimate atmospheric long wave radiation in the Northern Mato Grosso, Brazil." Ciência e Natura 42 (May 9, 2020): e105. http://dx.doi.org/10.5902/2179460x41205.

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The measures of Atmospheric Long Wave radiation are onerous, which brings the necessity to use alternative methods. Thus, the main aim of this paper was to test and parameterize some models that exist in the literature to estimate atmospheric long wave. The data were collected at Fazenda São Nicolau (2002 - 2003), located in Northwestern of Mato Grosso State. Data were processed hourly, monthly, and seasonal (dry and wet) besides clear and partly cloudy days on the average. The models of Swinbank, Idso Jackson, Idso, Prata and Duarte. were applied. The performance of the models was based on the mean error, square root of mean square error, absolute mean error, Pearson's coefficient and Willmott's coefficient. All models had presented high errors and low Peason’s and Willmott coefficients. After parameterizing, all models reduced their errors and increased Pearson and Willmott’s coefficient. The models of Idso and Swinbank had presented better and worse performance, respectively. It was not observed an increment on the performance of the model when classified according to cloudiness and seasonality. The Idso’s model had presented the lowest errors among the models. The model that had presented worst performance for any tested situation was Swinbank.

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Ericsson, Neil R., and Jaime R. Marquez. "Exact and Approximate Multi-Period Mean-Square Forecast Errors For Dynamic Econometric Models." International Finance Discussion Paper 1989, no. 348 (April 1989): 1–50. http://dx.doi.org/10.17016/ifdp.1989.348.

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Raun, W., M. Golden, J. Dhillon, D. Aliddeki, E. Driver, S. Ervin, M. Diaite-Koumba, et al. "Relationship between mean square errors and wheat grain yields in long-term experiments." Journal of Plant Nutrition 40, no. 9 (February 2017): 1243–49. http://dx.doi.org/10.1080/01904167.2016.1257638.

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Ramkrishna, D., and J. Swapna. "Characterization of Root-Mean-Square Acceleration Errors in Flexible Structures Undergoing Vibration Testing." Procedia Engineering 144 (2016): 482–92. http://dx.doi.org/10.1016/j.proeng.2016.05.159.

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Nakonechny, Alexander, Grigory Kudin, Petr Zinko, and Taras Zinko. "GUARANTEED ROOT-MEAN-SQUARE ESTIMATES OF LINEAR MATRIX TRANSFORMATIONS UNDER CONDITIONS OF STATISTICAL UNCERTAINTY." Journal of Automation and Information sciences 2 (March 1, 2021): 24–37. http://dx.doi.org/10.34229/1028-0979-2021-2-3.

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Linear estimation of observations in conditions of various types of interference in order to obtain unbiased estimates is the subject of research in numerous scientific publications. The problem of linear regression analysis in conditions when the elements of vector observations are known matrices that allow small deviations from the calculated ones was studied in previous publications of the authors. Using the technology of pseudo inverse operators, as well as the perturbation method, the problem was solved under the condition that linearly independent matrices are subject to small perturbations. The parameters of the linear estimates were presented in the form of expansions in a small parameter. Over the past decades, solving linear estimation problems under uncertainty has been carried out within the framework of the well-known minimax estimation method. Formally, the problems that arise in this direction are solved in the presence of some spaces for unknown observation parameters, as well as spaces to which observation errors may belong. The coefficients of the linear estimates are determined in the process of optimizing the guaranteed mean-square error of the desired estimate. Thus, the subject of scientific research can be problems of linear estimation of unknown rectangular matrices based on observations from errors with unknown correlation matrices of errors: unknown matrices belong to some bounded set, correlation matrices of random perturbations of the observation vector are unknown, but it is possible to assume cases when they belong to one or another defined bounded set. Some formulations of problems of linear estimation of observations are investigated in the proposed publication. The problem of linear estimation for a vector of observations of a special form is considered, the components of which are known rectangular matrices that are subject to small perturbations. Variants of the problem statement are proposed, which allow obtaining an analytical solution in the first approximation of a small parameter. A test example is presented.

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