A Second - Order Asymptotic Distributional Representation of M

A RESEARCH NOTE ON THE SECOND ORDER DIFFERENTIAL EQUATION

Let U(t, ) be solution of the Dirichlet problem y''+( t-q(t))y= 0 - 1 t l y(-l)= 0 = y(x), with variabIe t on (-1, x), for fixed x, which satisfies the initial condition U(-1, )=0 , (-1, )=1. In this paper, the asymptotic representation of the corresponding eigenfunctions of the eigen values has been investigated . Furthermore, the leading term of the asymptotic formula for ...

Second Order Asymptotic Distributional Representations of M - Estimators of General Parameters

Second order asymptotic distributional representations of M-estimators of general parameters are considered under appropriate (smoothness) conditions on the score function and the underlying distribution function. Parallel results for the one-step version of M-estimators are also studied. These results apply to the classical maximum likelihood estimators as well.

A remark on asymptotic enumeration of highest weights in tensor powers of a representation

We consider the semigroup $S$ of highest weights appearing in tensor powers $V^{otimes k}$ of a finite dimensional representation $V$ of a connected reductive group. We describe the cone generated by $S$ as the cone over the weight polytope of $V$ intersected with the positive Weyl chamber. From this we get a description for the asymptotic of the number of highest weights appearing in $V^{otime...

On the Infinite Product Representation of Solution and Dual Equation of Sturm-Liouville Equation with Turning Point of Order 4m+1

SECOND - ORDER ASYMPTOTIC RELAnONS AND GOODNESS - OF - FIT TESTS

For goodness-of-fit tests for a model (distribution) admitting nuisance location or scale parameters, second-order asymptotic distributional representations are exploited for some robust estimators that are asymptotically first-order equivalent; their difference then provides a goodness-of-fit test criterion, whose asymptotic properties are studied under the null hypothesis as well as under loc...