ON THE BEHAVIOR OF WALD STATISTICS FOR THE DISJUNCTION OF 2 REGULAR HYPOTHESES

Occasionally hypotheses arise which, although not themselves regular, have the logical structure of the disjunction of two, or in general se veral, regular hypotheses. An example of such a hypothesis is that of collapsibility in a three-way contingency table as defined by Whittemo re. When such a hypothesis is to be tested, a Wald test appears, super ficially, to offer a convenient solution. However, closer inspection r eveals that the irregularity intrinsic to such problems precludes the regularity conditions required for the valid construction of a Wald te st statistic. The purpose of this paper is to describe explicitly the nature of the irregularity and its effect on the asymptotic behaviour of the Wald test statistic.