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Unpublished Paper
Exact P-values for Discrete Models obtained by Estimation and Maximisation
MBS Working paper (2007)
  • Chris Lloyd, Melbourne Business School

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 null reduces this dependence. An approach somewhere between full maximisation and estimation is partial maximisation, with appropriate penalty, as introduced by Berger and Boos (1994). It is argued that estimation followed by maximisation is an attractive, but computationally more demanding, alternative to partial maximisation. We illustrate the ideas on a range of low dimension but important examples where the alternative methods can be investigated completely numerically.

  • nuisance parameters,
  • exact test,
  • tests of independence,
  • Behrens-Fisher problem,
  • matched pairs,
  • parametric bootstrap,
  • pre-pivoting,
  • pivotals
Publication Date
September, 2007
Citation Information
Chris Lloyd. "Exact P-values for Discrete Models obtained by Estimation and Maximisation" MBS Working paper (2007)
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