Interval estimation

Abstract

The use of a loss function focuses attention on one estimate of the parameter which appears to offer the ‘best bargain’. If we are more interested in plausible values of the parameter, we replace our single point estimate by a collection of points which, in the light of the data, is thought to contain the parameter. Such a collection is broadly known as a confidence region and the probability that it contains the parameter is its confidence coefficient. For individual parameters, such regions will be most useful if they are undivided intervals.