Composite transformation models: A fiducial perspective

✍ Scribed by Stephan Morgenthaler; Anna Nicolaou

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 466 KB
• Volume: 57
• Category: Article
• ISSN: 0378-3758
• DOI: 10.1016/s0378-3758(96)00035-3

✦ Synopsis

This paper discusses inferences for the parameters of a transformation model in the presence of a scalar nuisance parameter that describes the shape of the error distribution. The development is from the point of view of conditional inference and thus is an attempt to extend the classical fiducial (or structural inference) argument. For known shape parameter it is straightforward to derive a fiducial distribution of the transformation parameters from which confidence points can be obtained. For unknown shape parameter, the paper discusses a certain average of these fiducial distributions. The weights used in this averaging process are naturally induced by the action of the underlying group of transformations and correspond to a noninformative prior for the nuisance parameter. This results in a confidence distribution for the transformation parameters which in some cases has good frequentist properties. The method is illustrated by some examples.