UMP unbiased tests for multiparameter testing problems with restricted alternatives

Abstract.

Applications of the standard theory of UMP unbiased tests depends on conditions which in general are difficult to verify. In the present paper, however, we suggest more simple rules for applying this theory for regular exponential families of distributions. This approach leads to UMP unbiased tests for various multiparameter testing problems with restricted alternatives, and is shown to give justification for conditional tests for testing symmetry, diagonals-parameter symmetry and independence in two-way contingency tables. The derived tests are shown to possess attractive small sample properties.