Fiducial intervals of restricted parameters and their applications

In practice, the unknown parameters are often restricted. This paper provides a general method for constructing the fiducial intervals of the restricted parameters. Applying the general method, the fiducial intervals are constructed for the location (scale) parameters and the difference (ratio) of two locations (scales) in a location (scale) family of distributions. The frequency properties of these intervals are verified. For a variance components model, the fiducial intervals for the three parameters of common interest are obtained. Their frequency properties are investigated theoretically and computationally.