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Exact P-Values For Discrete Models Obtained By Estimation And Maximisation, Chris Lloyd

Chris J. Lloyd

In constructing exact tests, one must deal with the possible dependence of the P-value on the nuisance parameter/s psi as well as discreteness of the sample space. A classical but heavy handed approach is to maximise over psi. We prove what has previously been understood informally, namely that maximisation produces the uinique and smallest possible P-value subject to the ordering induced by the underlying test statistic and test validity. On the other hand, allowing for the worst case will be more attractive when the P-value is less dependent on psi. We investigate the extent to which estimating psi under the …