TESTING RANDOMNESS - Department of Mathematics and Statistics
TESTING RANDOMNESS - Department of Mathematics and Statistics
TESTING RANDOMNESS - Department of Mathematics and Statistics
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Optimal test<br />
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The optimal test <strong>of</strong> the null hypothesis<br />
linear statistics<br />
within the class <strong>of</strong><br />
is asymptotically normal both under the null hypothesis <strong>and</strong> the<br />
alternative<br />
.<br />
The Pitman efficiency <strong>of</strong> this statistic is determined by its efficacy, the<br />
distance between the means under the null hypothesis <strong>and</strong> the<br />
alternative, divided by the st<strong>and</strong>ard deviation (common to the null<br />
hypothesis <strong>and</strong> the alternative),<br />
Andrew Rukhin, NIST, UMBC – p.28/33
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