Confidence regions of minimal area for the scale-location parameter and their applications
Volume 28 / 2001
Applicationes Mathematicae 28 (2001), 125-142
MSC: Primary 62F25.
DOI: 10.4064/am28-2-1
Abstract
The area of a confidence region is suggested as a quality exponent of parameter estimation. It is shown that under very mild restrictions imposed on the underlying scale-location family there exists an optimal confidence region. Explicit formulae as well as numerical results concerning the normal, exponential and uniform families are presented. The question how to estimate the quantile function is also discussed.
