|
Abstract:
|
Suppose a large scale of independent and identical sequential probability ratio tests are conducted under normal observations with small same first-type and second-type error probabilities. An indifference zone [\theta_0, \theta_1=-\theta_0 ] is assumed for the design of the SPRT (\theta_0< 0). We consider the testing of existence and strength of sparse signals. First, it is shown that given that a null hypothesis is rejected, the mean estimate behaves the same asymptotically under both P_{\theta_0}(.) and P_{\theta_1}(.). Thus, the test for the existence of sparse signal depends on mainly the number of rejections. Second, given the number of rejections, the test for the strength of signal, or \theta>\theta_1 becomes a problem of testing for homogeneity under a mixture model. A combined local score test is thus proposed.
|
