In this technical report, we give detailed information about how to establish asymptotic theory for one-step weighted least-squares estimates of tensors, estimated eigenvalues and eigenvectors, and pseudo-likelihood ratio statistics. We establish the strong convergence rate and asymptotic normality for the one-step weighted least-squares estimates of tensors. We derive the first-order and secon...

We prove a quantitative estimate with power saving error term for the number of points in mapping class group orbit Teichmüller space that lie within metric ball given center and large radius. Estimates same kind are also proved sector bisector counts. These estimates effectivize asymptotic counting results Athreya, Bufetov, Eskin, Mirzakhani.

We discuss some aspects of recent research as well as more general issues about motivation, useful methods and open problems in the field of cosmological singularities. In particular, we review some of the approaches to the general area and include discussions of the method of asymptotic splittings, singularity and completeness theorems and the use of the Bel-Robinson energy to prove completene...

In a one parameter family of dilaton gravity theories which allow the coupling of the dilaton to gravity and to a U(1) gauge field to differ, we have found the existence of everywhere regular spacetimes describing black holes hiding expanding universes inside their horizon.

For the multivariate one-sample location model (relating to a diagonally symmetric distribution). sequential non-parametric (point as well as interval) estimators based on appropriate rank statistics are considered and their asymptotic properties studied. In this context. asymptotic risk-efficiency of the proposed estimators and asymptotic normality of the associated stopping times are establis...

the aim of this paper is to present a numerical method for singularly perturbed convection-diffusion problems with a delay. the method is a combination of the asymptotic expansion technique and the reproducing kernel method (rkm). first an asymptotic expansion for the solution of the given singularly perturbed delayed boundary value problem is constructed. then the reduced regular delayed diffe...

The asymptotic value, introduced by Kannai in 1966, is an asymptotic approach to the notion of the Shapley value for games with infinitely many players. A vector measure game is a game v where the worth v(S) of a coalition S is a function f of μ(S) where μ is a vector measure. Special classes of vector measure games are the weighted majority games and the two-house weighted majority games where...

In this paper, the asymptotic representation of the corresponding eigenfunctions of the eigenvalues has been investigated. Furthermore, we obtain the zeros of eigenfunctions.