Asymptotic linearity and limit distributions, approximations

Information Theoretic Asymptotic Approximations for Distributions of Statistics

We propose an information theoretic approach to approximating asymptotic distributions of statistics using the maximum entropy densities. Conventional maximum entropy densities are typically defined on a bounded support. For distributions defined on unbounded supports, we propose to use an asymptotically negligible dampening function for the maximum entropy approximation such that it is well de...

Asymptotic approximations to posterior distributions via conditional moment equations

We consider asymptotic approximations to joint posterior distributions in situations where the full conditional distributions referred to in Gibbs sampling are asymptotically normal. Our development focuses on problems where data augmentation facilitates simpler calculations, but results hold more generally. Asymptotic mean vectors are obtained as simultaneous solutions to fixed point equations...

Asymptotic Approximations for n !

Several approximations for n! have recently appeared in the literature. We show here how these approximations can be derived by expansion of certain polynomials in inverse powers of n and comparison with Stirling’s asymptotic series. Some new approximations are also given. The same procedure is applied to generate approximations for the ratio of two gamma functions.

Asymptotic distributions of Neumann problem for Sturm-Liouville equation

In this paper we apply the Homotopy perturbation method to derive the higher-order asymptotic distribution of the eigenvalues and eigenfunctions associated with the linear real second order equation of Sturm-liouville type on $[0,pi]$ with Neumann conditions $(y'(0)=y'(pi)=0)$ where $q$ is a real-valued Sign-indefinite number of $C^{1}[0,pi]$ and $lambda$ is a real parameter.

Limit spaces with approximations