CURRENT RESEARCH
TOPICS
EM P-values. The standard definition of a P-value for testing composite hypotheses
based on a statistic T is the tail probability maximised over the null. We
prove what has previously been understood informally, namely that this M-step
produces the smallest possible P-value subject to the ordering induced by T and
test validity. Thus, partially maximised P-values as suggested by Berger and
Boos (1994) are inadmissible. On the other hand, allowing for the worst case
through maximisation will be more attractive when the test statistic has
properties that are stable over the null hypothesis. We suggest replacement of
the unknown parameter by an estimate under the null and call this the E-step.
The resulting P-value is not valid until the M-step has been applied to produce
the EM P-value. The E-step can be applied more than once to further stablise
the properties of the test statistic. We illustrate the ideas on the
Behrens-Fisher problem and reproduce the better known exact solutions. We also
look at testing independence in a 2x2 table and show that the E-step is successful
in stabilising performance and that EM P-values appear to be more powerful, and
computationally less difficult, than other methods. A third draft of this paper is HERE and my
