See also
Estimator,
Estimator Bias,
Expectation Value,
Mean
Absolute Error,
Mean Absolute Percentage
Error,
Root-Mean-Square Error,
Variance
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References
Hyndman, R. J. and Koehler, A. B. "Another Look at Measures of Forecast Accuracy." Int. J. Forecasting 22,
679-688, 2006. https://doi.org/10.1016/j.ijforecast.2006.03.001.Iyanaga,
S. and Kawada, Y. (Eds.). "Statistical Estimation and Statistical Hypothesis
Testing." Appendix A, Table 23 in Encyclopedic
Dictionary of Mathematics. Cambridge, MA: MIT Press, pp. 1486-1489,
1980.Referenced on Wolfram|Alpha
Mean Square Error
Cite this as:
Weisstein, Eric W. "Mean Square Error."
From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MeanSquareError.html
Subject classifications
for observed values 
is the arithmetic mean
of the squared errors 
,
of a parameter 
, its mean square error is
![MSE(theta^^)=E[(theta^^-theta)^2]=Var(theta^^)+Bias(theta^^)^2,](/https/mathworld.wolfram.com/images/equations/MeanSquareError/NumberedEquation2.svg)
![E[Y]](/https/mathworld.wolfram.com/images/equations/MeanSquareError/Inline6.svg)
denotes the expectation value of 
. Thus mean square error combines the variance
and squared estimator bias. Its square
root is the root-mean-square error,
which has the same units as the measured quantity.
