School Seminars and Colloquia

More pivotal P-values through estimation and maximisation

Applied Statistics Seminar

by Chris Lloyd


Institution: Melbourne Business School
Date: Thu 16th March 2006
Time: 4:15 PM
Location: Theatre 1, Old Geology Building

Abstract: In constructing so-called exact tests, it is standard practice
to maximise the P-value with respect to any nuisance parameters. 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 the underlying test statistic and test validity. 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 replacing 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, which produces the EM
P-value. The E-step, which is a kind of parametric bootstrap, can be
applied more than once to further stablise the properties of the test
statistic. We illustrate the ideas on a range of examples. For the
Behrens-Fisher problem we reproduce the better known exact solutions. We
also look at three basic but important discrete statistical problems,
namely testing for a treatment effect in a 2 by 2 table, generated both
from independent samples or binary matched pairs as well as testing for
the effect of primary response on secondary response for binary matched
pairs with structural zero. In each of these examples, a limited
numerical study suggests that the E-step is successful in stabilising
performance and that EM P-values compare favourably with the partially
maximised P-values of Berger and Boos (1994).

For More Information: Owen Jones tel. 8344-6412 email: o.jones@ms.unimelb.edu.au