Title :
On one useful inequality in testing of hypotheses
Author :
Burnashev, Marat V.
Author_Institution :
Inst. of Problems of Inf. Transmission, Acad. of Sci., Moscow, Russia
fDate :
7/1/1998 12:00:00 AM
Abstract :
A simple proof of one probabilistic inequality is presented. Let P and Q be two given probability measures on a measurable space (𝒳, 𝒜). We consider testing of hypotheses P and Q using one observation. For an arbitrary decision rule, let α and β denote the two kinds of error probabilities. If both error probabilities have equal costs (or we want to minimize the maximum of them) then it is natural to investigate the minimal possible sum inf{α+β} for the best decision rule
Keywords :
decision theory; probability; decision rule; error probabilities; hypotheses testing; measurable space; observation; probabilistic inequality; probability measures; variational distance; Costs; Error probability; Extraterrestrial measurements; Information theory; Random processes; Random sequences; Testing;
Journal_Title :
Information Theory, IEEE Transactions on
