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A method for designing three-hypothesis test problems and sequential schemes. (English) Zbl 1205.62111
Summary: In applications, a two-sided hypothesis test problem sometimes needs to be changed to a three-hypotheses one with the two alternative hypotheses properly selected. We obtain the hypothesis design and a three-hypotheses sequential test scheme under the Koopman-Darmois distribution by solving a system of equations that meet requirements on the error rates and average sample number. This method provides a useful guide for practitioners to design hypotheses in multihypothesis test problems with controlled error rates and sampling cost. Formulas of the scheme’s error rates and average sample number are obtained using numerical quadrature for the discrete-time situation.
MSC:
62L10Sequential statistical analysis
62F03Parametric hypothesis testing
65C60Computational problems in statistics