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141 – Methods in Financial Risk Assessment
Game-Theoretic Decision-Making to Optimize Type-I and Type-II Errors in Statistical Hypothesis Testing
Mehmet Sahinoglu
Auburn University
Rasika Kelum Balasurya
Auburn University at Montgomery
David Tyson
Auburn University at Montgomery
What should constitute suitably small values of alpha and beta in tests of hypotheses? This is not a question to answer unequivocally for all situations. When establishing a test procedure to investigate statistically the credibility of a stated hypothesis, several factors must be considered one of which is the size of the sample. However, the most significant of all these factors is unquestionably to optimize Type I and II errors. Statisticians have by rule of thumb selected, such as a=0.05, none for ß depending on the alternative hypothesis at hand. Although, common logic usually played a major role such as in the case of testing null hypothesis of the patient being sick needs a fairly significant size of type I error lest we lose the patient if we reject that she is sick while she truly is sick and probably dying. But all these previous up-to-date arguments are not somewhat connected with cost or utility of producer's and consumer's risks in the sense of quality control or life sciences or in the cyber-risk domain or other manufacturing industries while testing a hypothesis of a good product vs. bad. This research innovatively outlines Game-theoretic approaches, such as that of von Neumann to this archaic problem to justify some optimal choices for a and ß when cost, utility and associated market factors are incorporated.