In this lecture I want delve a bit more deeply into the problem of comparing performance of various tests. Among other things I will try to provide an exposition of Chernoff’s (1952) result employed in Lars Hansen’s talks here several years ago. The lecture is based on van der Vaart (1998, Chapter 14). Consider the problem of testing H0 : θ ∈ Θ0 vs H1 : θ ∈ Θ1, using a test statistic Tn that re...

The Maschler–Owen consistent value for non-transferable utility games is axiomatized, by means of a marginality axiom. JEL Classification: C7, D7

Let f be a diffeomorphism of a closed C∞ manifold M . In this paper, we introduce the notion of the C1-stable specification property for a closed f -invariant set Λ of M , and we prove that f|Λ satisfies a C 1-stable specification property if and only if Λ is a hyperbolic elementary set. As a corollary, the C1-interior of the set of diffeomorphisms of M satisfying the specification property is ...

We show there is a residual set of non-Anosov C∞ Axiom A diffeomorphisms with the no cycles property whose elements have trivial centralizer. If M is a surface and 2 ≤ r ≤ ∞, then we will show there exists an open and dense set of of Cr Axiom A diffeomorphisms with the no cycles property whose elements have trivial centralizer. Additionally, we examine commuting diffeomorphisms preserving a com...

Rough set axiomatization is one aspect of rough set study to characterize rough set theory using dependable and minimal axiom groups. Thus, rough set theory can be studied by logic and axiom system methods. The classic rough set theory is based on equivalent relation, but rough set theory based on reflexive and transitive relation (called quasi-ordering) has wide applications in the real world....

Jan von Plato proposed in 1998 an intuitionist axiomatization of ordered affine geometry consisting 22 axioms. It is shown that axiom I.7, which equivalent to a conjunction four statements, two are redundant, can be replaced with simpler axiom, Plato’s Theorem 3.10.