Interval Estimation for the Ratio of Scale
Parameters
and for Ordered Scale Parameters
George Iliopoulos and Stavros Kourouklis
Confidence intervals for the ratio of scale parameters are constructed in
general families of distributions with nuisance (location) parameters. Each of
these intervals has coverage probability at least as large as that of the
standard minimum ratio of endpoints interval and, in addition, smaller ratio of
endpoints. Then analogous improved confidence intervals for the scale
parameters subject to order restriction are derived. The method of construction
is similar to that in Goutis and Casella
(1991, 1995). Examples are given and include the normal and exponential
distributions as well as the inverse Gaussian distribution which is not a
purely location-scale model. Applications to interval estimation of the error
variance in variance components models are also discussed.
AMS 1991 subject classifications: 62C99, 62F25.
Key words and phrases: Decision theory, scale parameter, confidence
interval, variance components.