  Let $X$ be a random vector with distribution $P_{\theta}$ where $\theta$ is
an unknown parameter. When estimating $\theta$ by some estimator $\varphi(X)$
under a loss function $L(\theta,\varphi)$, classical decision theory advocates
that such a decision rule should be used if it has suitable properties with
respect to the frequentist risk $R(\theta,\varphi)$. However, after having
observed $X=x$, instances arise in practice in which $\varphi$ is to be
accompanied by an assessment of its loss, $L(\theta,\varphi(x))$, which is
unobservable since $\theta$ is unknown. A common approach to this assessment is
to consider estimation of $L(\theta,\varphi(x))$ by an estimator $\delta$,
called a loss estimator. We present an expository development of loss
estimation with substantial emphasis on the setting where the distributional
context is normal and its extension to the case where the underlying
distribution is spherically symmetric. Our overview covers improved loss
estimators for least squares but primarily focuses on shrinkage estimators.
Bayes estimation is also considered and comparisons are made with unbiased
estimation.
