The Integrated Power Criterion and a Signal Detection Problem

In this paper, a new test criterion for binary decision problems is introduced. The integrated power function over a parameter interval is introduced as an extension of the power function. The concept of the most integrated powerful (MIP) test based on the integrated power function is introduced. The MIP criterion is to maximize the value of the integrated power function in any particular parameter interval. It is shown that the MIP test is the same as the uniformly most powerful (UMP) test for one-parameter exponential family. To illustrate the MIP test explicitly, some examples are included. As an application of the MIP test, the known signal detection problem is considered. The test statistic of the MIP detector for known signals is obtained and discussed, and an approximation of the MIP test statistic is also considered.