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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am28-2-1,
author = {A. Czarnowska and A. V. Nagaev},
title = {Confidence regions of minimal area for the scale-location parameter and their applications},
journal = {Applicationes Mathematicae},
volume = {28},
year = {2001},
pages = {125-142},
zbl = {1008.62567},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am28-2-1}
}
A. Czarnowska; A. V. Nagaev. Confidence regions of minimal area for the scale-location parameter and their applications. Applicationes Mathematicae, Tome 28 (2001) pp. 125-142. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am28-2-1/