Because the true population error $\epsilon(f)$ of a classifier cannot be observed directly in most practical scenarios, it must be estimated using samples. When a test dataset $\mathcal{D}$ is statistically representative of the underlying population, the empirical error $\epsilon_\mathcal{D}(f)$ serves as a statistical estimator for the population error $\epsilon(f)$. Since the empirical error is a sample average and the population error is its expectation, this reduces to a classical mean estimation problem.