Date of Award
Mathematics and Statistics
Nkurunziza, Severien (Mathematics & Statistics)
CC BY-NC-ND 4.0
In this thesis, we revisit some statistical problems, where classical inference can not provide small-sample optimal solution. These problems motivated Tsui and Weerahandi (1989), and Weerahandi (1993) to introduce the concepts of generalized inference which consist in constructing generalized test variable (GTV) and generalized pivotal quantity (GPQ). However, in general location-scale family, the existing literatures do not provide any systematic method for deriving these quantities. To overcome this problem, the equivariance principle is applied to construct GTV and GPQ in location-scale family. Namely, we construct the GPQ and GTV for the parameters of interest in one-sample and two-sample families cases. Particularly, we study inference problem concerning the difference between two location parameters. The simulation studies show that the suggested methods preserve the nominal level, and provides satisfactory power in small and moderate sample sizes. Finally, some real data sets are analyzed in order to illustrate the application of the suggested procedures.
Chen, Fuqi, "Equivariance and generalized inference in location-scale family" (2009). Electronic Theses and Dissertations. 349.