One-Sided Inference about Functionals of a Density

One-Sided Confidence About Functionals Over Tangent Cones

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 ...

Multiscale Inference about a Density

We introduce a multiscale test statistic based on local order statistics and spacings that provides simultaneous confidence statements for the existence and location of local increases and decreases of a density or a failure rate. The procedure provides guaranteed finite-sample significance levels, is easy to implement and possesses certain asymptotic optimality and adaptivity properties.

One-Sided Interval Trees

We give an alternative treatment and extension of some results of Itoh and Mahmoud on one-sided interval trees. The proofs are based on renewal theory, including a case with mixed multiplicative and additive renewals.

On One-Sided Ideals of Rings of Linear Transformations

A One-Sided Zimin Construction

A string is Abelian square-free if it contains no Abelian squares; that is, adjacent substrings which are permutations of each other. An Abelian square-free string is maximal if it cannot be extended to the left or right by concatenating alphabet symbols without introducing an Abelian square. We construct Abelian square-free finite strings which are maximal by modifying a construction of Zimin....