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Journal articles on the topic 'Mean error'

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1

Chai, T., and R. R. Draxler. "Root mean square error (RMSE) or mean absolute error (MAE)?" Geoscientific Model Development Discussions 7, no. 1 (February 28, 2014): 1525–34. http://dx.doi.org/10.5194/gmdd-7-1525-2014.

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Abstract. Both the root mean square error (RMSE) and the mean absolute error (MAE) are regularly employed in model evaluation studies. Willmott and Matsuura (2005) have suggested that the RMSE is not a good indicator of average model performance and might be a misleading indicator of average error and thus the MAE would be a better metric for that purpose. Their paper has been widely cited and may have influenced many researchers in choosing MAE when presenting their model evaluation statistics. However, we contend that the proposed avoidance of RMSE and the use of MAE is not the solution to the problem. In this technical note, we demonstrate that the RMSE is not ambiguous in its meaning, contrary to what was claimed by Willmott et al. (2009). The RMSE is more appropriate to represent model performance than the MAE when the error distribution is expected to be Gaussian. In addition, we show that the RMSE satisfies the triangle inequality requirement for a distance metric.
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2

Lee, Dominic, and Carey Priebe. "Exact mean and mean squared error of the smoothed bootstrap mean integrated squared error estimator." Computational Statistics 15, no. 2 (July 2000): 169–81. http://dx.doi.org/10.1007/s001800000026.

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3

Bar-Lev, Shaul K., Benzion Boukai, and Peter Enis. "On the mean squared error, the mean absolute error and the like." Communications in Statistics - Theory and Methods 28, no. 8 (January 1999): 1813–22. http://dx.doi.org/10.1080/03610929908832390.

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4

Khair, Ummul, Hasanul Fahmi, Sarudin Al Hakim, and Robbi Rahim. "Forecasting Error Calculation with Mean Absolute Deviation and Mean Absolute Percentage Error." Journal of Physics: Conference Series 930 (December 2017): 012002. http://dx.doi.org/10.1088/1742-6596/930/1/012002.

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5

Piegorsch, Walter W., and A. John Bailer. "Minimum mean-square error quadrature." Journal of Statistical Computation and Simulation 46, no. 3-4 (May 1993): 217–34. http://dx.doi.org/10.1080/00949659308811504.

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6

Tarter, Michael E. "Mean Integrated Squared Error Sampling." Journal of the American Statistical Association 81, no. 393 (March 1986): 234–42. http://dx.doi.org/10.1080/01621459.1986.10478266.

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7

Marron, J. S., and M. P. Wand. "Exact Mean Integrated Squared Error." Annals of Statistics 20, no. 2 (June 1992): 712–36. http://dx.doi.org/10.1214/aos/1176348653.

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8

Sedgwick, P. "Standard error of the mean." BMJ 340, mar17 1 (March 17, 2010): c1437. http://dx.doi.org/10.1136/bmj.c1437.

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9

Duan, Zhenyun. "MEAN ERROR EFFECT OF GEAR INTEGRATED ERROR MEASURING PROCESS." Chinese Journal of Mechanical Engineering 37, no. 02 (2001): 55. http://dx.doi.org/10.3901/jme.2001.02.055.

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10

Ohno, Shuichi, Teruyuki Shiraki, M. Rizwan Tariq, and Masaaki Nagahara. "Mean Squared Error Analysis of Quantizers With Error Feedback." IEEE Transactions on Signal Processing 65, no. 22 (November 15, 2017): 5970–81. http://dx.doi.org/10.1109/tsp.2017.2745450.

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11

TATEISHI, Ryutaro, and Chengang WEN. "Relationshio between Root Mean Square Error and Probable Error." Journal of the Japan society of photogrammetry and remote sensing 33, no. 4 (1994): 15–22. http://dx.doi.org/10.4287/jsprs.33.4_15.

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12

Monhor, D. "The arithmetic-geometric mean and the elliptic mean error." Acta Geodaetica et Geophysica Hungarica 38, no. 1 (February 2003): 53–60. http://dx.doi.org/10.1556/ageod.38.2003.1.8.

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13

Figueroa-López, José E., and Cecilia Mancini. "Optimum thresholding using mean and conditional mean squared error." Journal of Econometrics 208, no. 1 (January 2019): 179–210. http://dx.doi.org/10.1016/j.jeconom.2018.09.011.

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14

Garg, Pankaj Kumar, and Debajyoti Mohanty. "Mean (Standard Deviation) or Mean (Standard Error of Mean): Time to Ponder." World Journal of Surgery 37, no. 4 (November 30, 2012): 932. http://dx.doi.org/10.1007/s00268-012-1854-z.

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15

Yatracos, Yannis G. "On prediction and mean squared error." Canadian Journal of Statistics 20, no. 2 (June 1992): 187–200. http://dx.doi.org/10.2307/3315467.

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16

Rao, J. N. K., Jiming Jiang, and Kalyan Das. "Mean squared error of empirical predictor." Annals of Statistics 32, no. 2 (April 2004): 818–40. http://dx.doi.org/10.1214/009053604000000201.

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17

Schmidt, David A., Michael Joham, and Wolfgang Utschick. "Minimum mean square error vector precoding." European Transactions on Telecommunications 19, no. 3 (2008): 219–31. http://dx.doi.org/10.1002/ett.1192.

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18

Song, Wheyming Tina, and Bruce W. Schmeiser. "Optimal Mean-Squared-Error Batch Sizes." Management Science 41, no. 1 (January 1995): 110–23. http://dx.doi.org/10.1287/mnsc.41.1.110.

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19

Rougier, Jonathan. "Ensemble Averaging and Mean Squared Error." Journal of Climate 29, no. 24 (November 23, 2016): 8865–70. http://dx.doi.org/10.1175/jcli-d-16-0012.1.

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Abstract In fields such as climate science, it is common to compile an ensemble of different simulators for the same underlying process. It is a striking observation that the ensemble mean often outperforms at least half of the ensemble members in mean squared error (measured with respect to observations). In fact, as demonstrated in the most recent IPCC report, the ensemble mean often outperforms all or almost all of the ensemble members across a range of climate variables. This paper shows that these could be mathematical results based on convexity and averaging but with implications for the properties of the current generation of climate simulators.
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20

Beheshti, Soosan, Masoud Hashemi, Ervin Sejdic, and Tom Chau. "Mean Square Error Estimation in Thresholding." IEEE Signal Processing Letters 18, no. 2 (February 2011): 103–6. http://dx.doi.org/10.1109/lsp.2010.2097590.

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21

Fišerová, Eva, and Martin Kubala. "Mean fluorescence lifetime and its error." Journal of Luminescence 132, no. 8 (August 2012): 2059–64. http://dx.doi.org/10.1016/j.jlumin.2012.03.038.

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22

Chatfield, Chris. "Apples, oranges and mean square error." International Journal of Forecasting 4, no. 4 (January 1988): 515–18. http://dx.doi.org/10.1016/0169-2070(88)90127-6.

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23

Cao, R. "Bootstrapping the Mean Integrated Squared Error." Journal of Multivariate Analysis 45, no. 1 (April 1993): 137–60. http://dx.doi.org/10.1006/jmva.1993.1030.

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24

Frías-Paredes, Laura, Fermin Mallor, Martín Gastón-Romeo, and Teresa León. "Dynamic mean absolute error as new measure for assessing forecasting errors." Energy Conversion and Management 162 (April 2018): 176–88. http://dx.doi.org/10.1016/j.enconman.2018.02.030.

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25

Salimov, R. F., I. N. Volodin, and N. F. Nasibullina. "Sequential d-guaranteed estimate of the normal mean with bounded relative error." Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki 161, no. 1 (2019): 145–51. http://dx.doi.org/10.26907/2541-7746.2019.1.145-151.

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26

Torabi, Mahmoud, and Jon N. K. Rao. "Mean squared error estimators of small area means using survey weights." Canadian Journal of Statistics 38, no. 4 (October 19, 2010): 598–608. http://dx.doi.org/10.1002/cjs.10078.

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27

Magnussen, S., G. Frazer, and M. Penner. "Alternative mean-squared error estimators for synthetic estimators of domain means." Journal of Applied Statistics 43, no. 14 (February 17, 2016): 2550–73. http://dx.doi.org/10.1080/02664763.2016.1142942.

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28

Guo, Meixi, and Malay Ghosh. "Mean squared error of James–Stein estimators for measurement error models." Statistics & Probability Letters 82, no. 11 (November 2012): 2033–43. http://dx.doi.org/10.1016/j.spl.2012.06.019.

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29

Correll, Michael, and Michael Gleicher. "Error Bars Considered Harmful: Exploring Alternate Encodings for Mean and Error." IEEE Transactions on Visualization and Computer Graphics 20, no. 12 (December 31, 2014): 2142–51. http://dx.doi.org/10.1109/tvcg.2014.2346298.

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30

Chai, T., and R. R. Draxler. "Root mean square error (RMSE) or mean absolute error (MAE)? – Arguments against avoiding RMSE in the literature." Geoscientific Model Development 7, no. 3 (June 30, 2014): 1247–50. http://dx.doi.org/10.5194/gmd-7-1247-2014.

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Abstract. Both the root mean square error (RMSE) and the mean absolute error (MAE) are regularly employed in model evaluation studies. Willmott and Matsuura (2005) have suggested that the RMSE is not a good indicator of average model performance and might be a misleading indicator of average error, and thus the MAE would be a better metric for that purpose. While some concerns over using RMSE raised by Willmott and Matsuura (2005) and Willmott et al. (2009) are valid, the proposed avoidance of RMSE in favor of MAE is not the solution. Citing the aforementioned papers, many researchers chose MAE over RMSE to present their model evaluation statistics when presenting or adding the RMSE measures could be more beneficial. In this technical note, we demonstrate that the RMSE is not ambiguous in its meaning, contrary to what was claimed by Willmott et al. (2009). The RMSE is more appropriate to represent model performance than the MAE when the error distribution is expected to be Gaussian. In addition, we show that the RMSE satisfies the triangle inequality requirement for a distance metric, whereas Willmott et al. (2009) indicated that the sums-of-squares-based statistics do not satisfy this rule. In the end, we discussed some circumstances where using the RMSE will be more beneficial. However, we do not contend that the RMSE is superior over the MAE. Instead, a combination of metrics, including but certainly not limited to RMSEs and MAEs, are often required to assess model performance.
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31

Magnussen, Steen. "A New Mean Squared Error Estimator for a Synthetic Domain Mean." Forest Science 63, no. 1 (February 17, 2017): 1–9. http://dx.doi.org/10.5849/forsci.16-056.

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32

Simaan, Majeed, Yusif Simaan, and Yi Tang. "Estimation error in mean returns and the mean-variance efficient frontier." International Review of Economics & Finance 56 (July 2018): 109–24. http://dx.doi.org/10.1016/j.iref.2017.10.019.

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33

Yonghe, Deng. "Perfectively Deducing Bessel Mean Square Error Formula." Open Civil Engineering Journal 9, no. 1 (July 31, 2015): 423–25. http://dx.doi.org/10.2174/1874149501509010423.

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In the survey teaching materials of China, deducing Bessel mean square error formula is all based on survey values with same mathematical expectation. These methods aren’t perfect. So, based on survey values without same mathematics expectation to prove Bessel mean square error formula is very necessary. Therefore, considering different mathematical expectation, it is meaningful that this paper has perfectively deduced Bessel mean square error formula.
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34

Roll, Richard. "A Mean/Variance Analysis of Tracking Error." Journal of Portfolio Management 18, no. 4 (July 31, 1992): 13–22. http://dx.doi.org/10.3905/jpm.1992.701922.

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35

Li, Rui, and Saralees Nadarajah. "Mean and variance of round off error." Signal Processing 127 (October 2016): 185–90. http://dx.doi.org/10.1016/j.sigpro.2016.03.007.

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36

de Myttenaere, Arnaud, Boris Golden, Bénédicte Le Grand, and Fabrice Rossi. "Mean Absolute Percentage Error for regression models." Neurocomputing 192 (June 2016): 38–48. http://dx.doi.org/10.1016/j.neucom.2015.12.114.

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37

Lopez-Valcarce, R. "Realizable minimum mean-squared error channel shorteners." IEEE Transactions on Signal Processing 53, no. 11 (November 2005): 4354–62. http://dx.doi.org/10.1109/tsp.2005.857050.

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38

Petra, Nicola, Davide De Caro, Valeria Garofalo, Ettore Napoli, and Antonio G. M. Strollo. "Truncated squarer with minimum mean-square error." Microelectronics Journal 45, no. 6 (June 2014): 799–804. http://dx.doi.org/10.1016/j.mejo.2014.02.018.

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39

Abel, J. S. "A bound on mean-square-estimate error." IEEE Transactions on Information Theory 39, no. 5 (1993): 1675–80. http://dx.doi.org/10.1109/18.259655.

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40

Jianjun, Zhu. "Robust estimate with minimum mean squared error." Australian Surveyor 36, no. 2 (June 1991): 111–15. http://dx.doi.org/10.1080/00050326.1991.10438723.

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41

Stoughton, Roland, and Stewart Strait. "Source imaging with minimum mean‐squared error." Journal of the Acoustical Society of America 94, no. 2 (August 1993): 827–34. http://dx.doi.org/10.1121/1.408184.

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42

KOBAYASHI, Kazuo. "Two Dissimilar Semantics of Mean Square Error." Journal of the Japan society of photogrammetry and remote sensing 30, no. 3 (1991): 42–48. http://dx.doi.org/10.4287/jsprs.30.3_42.

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43

Yokota, Yasunari, and Motoki Shiga. "An entropy estimator improving mean squared error." Electronics and Communications in Japan (Part III: Fundamental Electronic Science) 87, no. 9 (2004): 1–10. http://dx.doi.org/10.1002/ecjc.10163.

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44

Lee, Ming Ha, and Michael B. C. Khoo. "The Synthetic Mean Square Error Control Chart." Communications in Statistics - Simulation and Computation 43, no. 6 (December 2, 2013): 1523–42. http://dx.doi.org/10.1080/03610918.2012.735321.

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45

Fuleky, Peter, and Luigi Ventura. "Mean lag in general error correction models." Economics Letters 143 (June 2016): 107–10. http://dx.doi.org/10.1016/j.econlet.2016.03.028.

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46

-T. Leung, J. Y., T. W. Tam, C. S. Wong, and G. H. Young. "Minimizing Mean Flow Time with Error Constraint." Algorithmica 20, no. 1 (January 1998): 101–18. http://dx.doi.org/10.1007/pl00009185.

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47

Salman, Mohammad Shukri, Osman Kukrer, and Aykut Hocanin. "Recursive inverse algorithm: Mean-square-error analysis." Digital Signal Processing 66 (July 2017): 10–17. http://dx.doi.org/10.1016/j.dsp.2017.04.001.

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48

Ljung, Lennart, and Pierre Priouret. "Remarks on the mean square tracking error." International Journal of Adaptive Control and Signal Processing 5, no. 6 (November 1991): 395–403. http://dx.doi.org/10.1002/acs.4480050605.

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49

Wang, Weijie, and Yanmin Lu. "Analysis of the Mean Absolute Error (MAE) and the Root Mean Square Error (RMSE) in Assessing Rounding Model." IOP Conference Series: Materials Science and Engineering 324 (March 2018): 012049. http://dx.doi.org/10.1088/1757-899x/324/1/012049.

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50

Dalton, Lori A., and Edward R. Dougherty. "Optimal mean-square-error calibration of classifier error estimators under Bayesian models." Pattern Recognition 45, no. 6 (June 2012): 2308–20. http://dx.doi.org/10.1016/j.patcog.2011.12.003.

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