In statistical decision theory the loss function $L(\theta, a)\ge-K > -\infty$ is often chosen for technical convenience (e.g. See  p.3 ). Can anyone explain why the above condition is convenient, and if it is feasible, provide a simple example.
If loss is not bounded below, there is no admissible estimator. An admissible estimator is desirable because it precludes stupid estimators like the Hodge's superefficient estimator. Hodge's estimator is "better on paper" than the MLE (unbiased yet MORE efficient) but in fact it isn't. The risk behaves erratically and can explode to infinity for probability models where the truth approaches the null.