Under the given hypothesis, every graded prime submodule which contains N2(resp. K2) contains N1 resp. K1).
In the original detection problem to be solved in (5), we need to estimate the unknowns {μ0,Σ0} under hypothesis ℋ 0, as well as the unknowns {μ1,Σ1} under hypothesis ℋ 1.
Hence, a common practice is to choose the threshold based on under hypothesis.
We obtain the probability distribution of observing a given residual error under the null hypothesis, for every possible number of frequency points.
Under the hypothesis of Theorem 4, every finite order entire solution of (7) has no wandering domains.
Under these hypotheses, every bounded subset is weakly relatively compact (see [4]), which implies that (H1) is true.
In addition, under Hypothesis 2.2 for every k ≥ N 0 + 1, we have the representations D k = { P k + R k V R k , V ∈ V }, C k = { P k + R k U R k , U ∈ U }. Consequently, the Weyl disks D k are closed and convex for every k ≥ N 0 + 1. Proof The result follows from (4.15), (4.16), and (4.17) combined with Corollary 4.5.
Therefore, the value of T should tend to be larger under the alternative hypothesis than under the null hypothesis.
The likelihood ratio compares the maximum likelihood of the data under the null hypothesis versus that under the alternative hypothesis.
Under alternative hypothesis, the test statistic diverges.
Insets show two examples of adaptive convergence and divergence under each hypothesis.
