Martin Larsson (Carnegie Mellon University)
Title: E-variables for hypotheses generated by constraints
Abstract: There is a natural convex duality relationship between a statistical
hypothesis and its set of e-variables. If the hypothesis is defined
through a collection of linear constraints, often understood as
(generalized) moment restrictions, then one expects that any e-variable
can be expressed in terms of convex combinations of the constraint
functions. In simple situations, such as for finite sample spaces,
results of this kind can be proved by convex duality in Euclidean space.
However, in more general cases the situation is less clear. In this talk
I will show that e-variable representations of the kind described above
hold in arbitrary sample spaces, without any regularity conditions or
other assumptions whatsoever. I will also discuss a number of examples
illustrating how the abstract theory instantiates in concrete cases.
