
Point and region estimation may both be described as specific decision problems. In point estimation,
the action space is the set of possible values of the quantity on interest; in region estimation, the action
space is the set of its possible credible regions. Foundations dictate that the solution to these decision
problems must depend on both the utility function and the prior distribution. Estimators intended for
general use should surely be invariant under onetoone transformations, and this requires the use
of an invariant loss function; moreover, an objective solution requires the use of a prior which does
not introduce subjective elements. The combined use of an invariant informationtheory based loss
function, the intrinsic discrepancy, and an objective prior, the reference prior, produces a general
solution to both point and region estimation problems. In this paper, estimation of the two parameters
of univariate locationscale models is considered in detail from this point of view, with special attention
to the normal model. The solutions found are compared with a range of conventional solutions.
