Abstract
On our Web-page we posed the question “Can it happen that a uniformly most powerful (UMP-) test (with fixed sample size) may be improved by simple randomization?” (Schmitz (1999)) and, later on, gave an affirmative answer via a simple example where the power functions coincide for n = 2 and 3. Here we characterize all testing problems with i.i.d. random variables where an additional observation fails to improve the power.
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Konopka, J., Schmitz, N. Redundant observations at testing i.i.d. random variables. Statistical Papers 43, 595–602 (2002). https://doi.org/10.1007/s00362-002-0127-6
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DOI: https://doi.org/10.1007/s00362-002-0127-6