11.4 Likelihood Ratio Tests
In the previous sections, UMP tests were constructed for several important hypotheses and were illustrated by specific examples. Those tests have the UMP property, provided the underlying p.d.f. is of the Exponential type given in (4). What happens if either the p.d.f. is not of this form and/or the hypotheses to be tested are not of the type for which UMP tests exist? One answer is for sure that the testing activities will not be terminated here; other procedures are to be invented and investigated. Such a procedure is one based on the Likelihood Ratio (LR), which gives rise to the so-called LR tests. The rationale behind this procedure was given in Section 3 of Chapter 8. What we are doing in this section is to ...
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