Let $X_1,...,X_n$ be some observations, and let $\theta$ be some parameter of the density function we want to estimate.
Then, it is well known that
$l(\theta) = n^{-1} \sum_{i=1}^n \log f(X_i ; \theta)$ is called the average log-likelihood.
What is $\mathbb{E}[\log f(X_1 ; \theta)]$ called? Meaning, "the expected value of the likelihood"? It can be called the cross-entropy, or perhaps it has other name, but it seems to me it should have a name relating it to the likelihood, such as "population likelihood" perhaps or something of that sort.
Anyone knows? Wikipedia did not help much here.