ASYMPTOTIC DERIVATION OF Z* STATISTIC

Asymptotic Expansions of Thelikelihood Ratio Test Statistic

SUMMARY. Likelihood ratio tests are used to test ordered hypotheses involving the parameters of k independent samples from an exponential family. For the test of constancy of the parameters versus an ordered alternative, the likelihood ratio test statistic is asymptotically distributed as a mixture of k chi-squared distributions under the null hypothesis. This paper derives an asymptotic expans...

Asymptotic behavior of discrete holomorphic maps z and log(z)

It is shown that discrete analogs of z and log(z), defined via particular “integrable” circle patterns, have the same asymptotic behavior as their smooth counterparts. These discrete maps are described in terms of special solutions of discrete Painlevé-II equations, asymptotics of these solutions providing the behaviour of discrete z and log(z) at infinity.

Asymptotic normality of the posterior given a statistic

The authors establish the asymptotic normality and determine the limiting variance of the posterior density for a multivariate parameter, given the value of a consistent and asymptotically Gaussian statistic satisfying a uniform local central limit theorem. Their proof is given in the continuous case but generalizes to lattice-valued random variables. It hinges on a uniform Edgeworth expansion ...

An Asymptotic Derivation of Weakly Nonlinear Ray Theory

Using a method of expansion similar to Chapman Enskog expansion, a new formal perturbation scheme based on high frequency approximation has been constructed. The scheme leads to an eikonal equation in which the leading order amplitude appears. The transport equation for the amplitude has been deduced with an error O(ǫ2) where ǫ is the small parameter appearing in the high frequency approximatio...

Behavior of poroelastic isotropic beam derivation by asymptotic expansion method