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Zbl 1205.62111
Li, Yan; Pu, Xiaolong
A method for designing three-hypothesis test problems and sequential schemes. (English)
[J] Commun. Stat., Simulation Comput. 39, No. 8-10, 1690-1708 (2010). ISSN 0361-0918; ISSN 1532-4141/e

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 2000:: *62L10 Sequential statistical analysis
62F03 Parametric hypothesis testing
65C60 Computational problems in statistics

Keywords: average sample number; numerical quadrature; sequential scheme; three-hypothesis test

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