Error metrics

Root Mean Squared error

A typical way of measuring the difference between observations and results from a predictor.

The formal definition is:

\[ \begin{aligned} RMSE(\hat{\theta}) &= \sqrt{\operatorname{MSE}(\hat{\theta})} \\ &= \sqrt{\operatorname{E}((\hat{\theta}-\theta)^2)}. \end{aligned} \]

For \(N\) observations \(Y=\{y_1,\dots,y_N\}\) we can express it as:

\[ RMSE=\sqrt{\frac{\sum_{n=1}^{N}({\hat {y}}_{n}-y_{n})^{2}}{N}}. \]