Question
Let S be a statistic. Recall from class: A test is called an upper S-test if it is of the form = 1[S > a]
Let S be a statistic. Recall from class: A test is called an upper S-test if it is of the form = 1[S > a] + b1[S = a] for some real a and some 0 b 1.
A test is called a lower S-test if it is of the form = 1[S < a] + b1[S = a]. for some real a and some 0 b 1.
Show the following
(1) If is an upper S-test, then 1 is a lower S-test.
(2) If is a lower S-test, then 1 is an upper S-test.
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A First Course in General Relativity
Authors: Bernard Schutz
2nd edition
521887054, 978-0521887052
