Consider the samples x1, …, xN which satisfy the following model (see the attachment).
x_n – sqrt(0) + w_n; n = 1, …, N
where [w_n] is i.i.d. with corresponding pdf f(w). We are interested in distinguishing between the two hypothesis Ho: theta = 0 and H1: theta > 0. Examine whether a locally optimum test exists that can solve this hypothesis testingproblem. b) In case your answer is NO in the previous question, redefine, in a simple way, your problem so that you can obtain a locally optimum solution.
In the following, “Notes” = the text in file “stat450notes11 1”
We assume that “locally optimum test” translates to English as “locally most powerful test” = …
The solution solves a hypothesis testing problem and locally optimum test.