One-Sided Confidence About Functionals Over Tangent Cones
نویسنده
چکیده
In the setup of i.i.d. observations and a real valued differentiable functional T , locally asymptotic upper bounds are derived for the power of one-sided tests (simple, versus large values of T ) and for the confidence probability of lower confidence limits (for the value of T ), in the case that the tangent set is only a convex cone. The bounds, and the tests and estimators which achieve the bounds, are based on the projection of the influence curve of the functional on the closed convex cone, as opposed to its closed linear span. The higher efficiency comes along with some weaker, only one-sided, regularity and stability.
منابع مشابه
An In nite Class of Convex Tangent Cones
Since the early 1970's there have been many papers devoted to tangent cones and their applications to optimization. Much of the debate over which tangent cone is \best" has centered on the properties of Clarke's tangent cone and whether other cones have these properties. In this paper it is shown that there are an innnite number of tangent cones with some of the nicest properties of Clarke's co...
متن کاملThe Tangent Cones at Double points of Prym-Canonical Divisors of Curves of genus 7
Let η be a line bundle on a smooth curve X with η^2=0 such that π_η, the double covering induced by η is an etale morphism. Assume also that X_η be the Prym-canonical model of X associated to K_X.η and Q is a rank 4 quadric containing X_η. After stablishing the projective normality of the prym-canonical models of curves X with Clifford index 2, we obtain in this paper a sufficient condition for...
متن کاملConfidence Intervals for the Power of Two-Sided Student’s t-test
For the power of two-sided hypothesis testing about the mean of a normal population, we derive a 100(1 − alpha)% confidence interval. Then by using a numerical method we will find a shortest confidence interval and consider some special cases.
متن کاملFacially Dual Complete (nice) Cones and Lexicographic Tangents
We study the boundary structure of closed convex cones, with a focus on facially dual complete (nice) cones. These cones form a proper subset of facially exposed convex cones, and they behave well in the context of duality theory for convex optimization. Using the wellknown and very commonly used concept of tangent cones in nonlinear optimization, we introduce some new notions for exposure of f...
متن کاملReal Algebraic Varieties with Prescribed Tangent Cones
The definition of the tangent cone C(V, p) to an algebraic variety V at a point p was given by Whitney more than 40 years ago as one of the tools to get information about the geometric shape of a variety near a singular point. While the complex case has been widely and successfully studied, including from a computational point of view, only recently have some first attempts been made to elucida...
متن کامل