Question: 21. (i) The following example shows that a-admissibility does not always imply d-admissibility. Let X be distributed as U(O, 8), and consider the tests !PI

21. (i) The following example shows that a-admissibility does not always imply d-admissibility. Let X be distributed as U(O, 8), and consider the tests !PI and !P2 which reject when respectively X < 1 and X < t for testing H : 8 = 2 against K : 8 = 1. Then for a = ~, !PI and !P2 are both a-admissible but !P2 is not d-admissible. (ii) Verify the existence of the test !Po of Example 12.

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