Risk function

Frequentist expected loss

We first define the expected loss in the frequentist context. It is obtained by taking the expected value with respect to the probability distribution, ${\displaystyle P_{\theta }}$, of the observed data, ${\displaystyle X}$. This is also referred to as the risk function of the decision rule ${\displaystyle \delta }$ and the parameter ${\displaystyle \theta }$. Here the decision rule depends on the outcome of ${\displaystyle X}$. The risk function is given by: