Mean squared error - Aetherwisp

The mean squared error or mean squared deviation of a sample is the mean of the squares of the errors:

\text{MSE}=\frac{1}{N}\sum_{i=1}^{N} (x_{i}-\hat{\mu})^{2}

where $x_{i}$ is the $i$ -th sample, $\hat{\mu}$ is the sample mean and $N$ is the sample size. Alternatively, in the case of an estimator over the sample, it can also be written as

\text{MSE}=b^{2}+\hat{\sigma} ^{2}

where $b$ is the bias of the estimator and $\hat{\sigma}^{2}$ is the sample variance. If the estimator is unbiased, it coincides with the sample Variance.