Journal of Probability and Statistics
Volume 2011 (2011), Article ID 474826, 16 pages
Research Article

Equivariance and Generalized Inference in Two-Sample Location-Scale Families

Department of Mathematics and Statistics, University of Windsor, 401 Sunset Avenue, Windsor, ON, Canada N9B 3P4

Received 17 May 2011; Revised 15 August 2011; Accepted 15 August 2011

Academic Editor: Ricardas Zitikis

Copyright © 2011 Sévérien Nkurunziza and Fuqi Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We are interested in-typical Behrens-Fisher problem in general location-scale families. We present a method of constructing generalized pivotal quantity (GPQ) and generalized value (GPV) for the difference between two location parameters. The suggested method is based on the minimum risk equivariant estimators (MREs), and thus, it is an extension of the methods based on maximum likelihood estimators and conditional inference, which have been, so far, applied to some specific distributions. The efficiency of the procedure is illustrated by Monte Carlo simulation studies. Finally, we apply the proposed method to two real datasets.