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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 (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

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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 (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 unsystema

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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 (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 (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 (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 (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

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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 er

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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 (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.

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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) (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 kesala

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24

Pereira, Janser Moura, Joel Augusto Muniz, and Carlos Alberto Silva. "Nonlinear models to predict nitrogen mineralization in an Oxisol." Scientia Agricola 62, no. 4 (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 p

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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 (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 (1993): 642–44. http://dx.doi.org/10.1002/for.3980120805.

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27

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

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28

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 (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 exam

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29

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 (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 occurr

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30

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 (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 (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 relativ

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32

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 (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 err

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33

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 autor

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34

Yang, Xiaosong, Timothy DelSole, and Hua-Lu Pan. "Empirical Correction of the NCEP Global Forecast System." Monthly Weather Review 136, no. 12 (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 tim

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35

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 m

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36

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

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37

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 as

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38

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 (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, z

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39

ناصر, جنان عباس. "Comparison Bayes Estimators of Reliability in the Exponential Distribution." Journal of Economics and Administrative Sciences 24, no. 104 (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 usin

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40

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 (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

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41

Lee, Stephen Man Sing. "Optimal choice between parametric and non-parametric bootstrap estimates." Mathematical Proceedings of the Cambridge Philosophical Society 115, no. 2 (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 asymptoti

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42

Alam, S. M. Mahfuz, and Mohd Hasan Ali. "Equation Based New Methods for Residential Load Forecasting." Energies 13, no. 23 (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

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43

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 (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 Greenl

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44

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 o

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45

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 (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 th

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46

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 th

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47

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 (1989): 1–50. http://dx.doi.org/10.17016/ifdp.1989.348.

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48

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

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49

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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50

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 perturbati

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