An optimal multiple decision rule for signs of parameters.
The problem of simultaneously deciding the signs of p parameters based on normally distributed estimators is considered. A decision that a parameter is too close to zero to decide its sign is allowed in order that the probability of at least one incorrect decision can be kept less than a preassigned value. Concepts of upper-convexity and local optimality are defined, and for p = 2 or 3 the locally optimal rules in the class of upper-convex rules are found. Critical values and operating characteristics are given for the locally optimal rule and some other plausible rules when p = 2.
Bohrer
R
R
Statistical Laboratory, University of California, Berkeley, California 94720.
Schervish
M J
MJ