The mean squared error of an estimator of a parameter is the expected value of the square of the difference between the estimator and the parameter. In symbols, if X is an estimator of the parameter t, then

MSE(X) = E( (X−t)² ).

The MSE measures how far the estimator is off from what it is trying to estimate, on the average in repeated experiments. It is a summary measure of the accuracy of the estimator. It combines any tendency of the estimator to overshoot or undershoot the truth (bias), and the variability of the estimator (SE). The MSE can be written in terms of the bias and SE of the estimator:

MSE(X) = (bias(X))² + (SE(X))².