M-statistics

Chapter 4-value and duality

First, we introduce a new definition of the -value for the double-sided hypothesis, which is especially important for asymmetric distributions. This definition implies that under the null hypothesis, the distribution of the -value is uniform on and under the alternative yields the power functions defined in the previous chapters: equal-tail, DL, and unbiased test. Second, following the duality principle between CI and hypothesis test, we derive specific forms of the test dual to CI and CI dual to test for the MC and MO-statistics. Finally, the M-statistics for exact statistical inference is overviewed in the last section, accompanied by the table of major equations.

4.1 -value for the double-sided hypothesis

There are two paradigms of statistical hypothesis testing, known by the names of the great statisticians, Fisher, Neyman and Pearson. While the latter operates with the power function the former solely relies on the computation of the -value. The two ...