We consider quadratic forms Q n = X 1j<kn a jk X j X k ; where X j are i.i.d. random variables with nite third moment. We obtain optimal bounds for the Kolmogorov distance between the distribution of Q n and the distribution of the same quadratic forms with X j replaced by corresponding Gaussian random variables.

This article proposes a new general methodology for constructing nonparametric asymptotic distribution-free tests for semiparametric hypotheses in regression models. Tests are based on the difference between the estimated restricted and unrestricted regression errors’ distributions. A suitable integral transformation of this difference renders the tests asymptotically distribution-free, with li...

The distributions of vertex degrees in random recursive trees and random plane recursive trees are shown to be asymptotically normal. Formulas are given for the asymptotic variances and covariances of the number of vertices with given outdegrees. We also give functional limit theorems for the evolution as vertices are added. The proofs use some old and new results about generalized Pólya urn mo...

0.1 Asymptotic Distribution for Conditional MLE of VARMA Models For a well-defined stationary and invertible VARMA(p, q) model, we assume that the innovations {at} satisfies (a) E(at|Ft−1) = 0, (b) E(atat|Ft−1) = Σ > 0, and (c) at has finite fourth moments, where Ft−1 denotes the σ-field generated by {zt−1, zt−2, · · ·}. It has been proven (Dunsmuir and Hannan, 1976, and Hannan and Deistler, 19...

We consider the Useful Informational Energy introduced by L. Pardo [5]. Our purpose is to study the asymptotic distribution of its analogue estimator, in a random and stratified sampling, as well as its application to testing hypotheses.

Service-oriented Architectures (SOA) facilitate the dynamic and seamless integration of services offered by different service providers which in addition can be located in different trust domains. Especially for business integration scenarios, Federated Identity Management emerged as a possibility to propagate identity information as security assertions across company borders in order to secure...

analysis of aperture-coupled microstrip antennas with a superstrate using space domain closed form greens functions is presented. integral equations are derived from applying the boundary conditions on the radiating patch, across the aperture, and on the microstrip feedline. the computation of space domain greens functions is performed using the closed-form. the solution of the integral equatio...

In this paper, we obtain the strong consistency and asymptotic distribution of the Theil-Sen estimator in simple linear regression models with arbitrary error distributions. We show that the Theil-Sen estimator is super-efficient when the error distribution is discontinuous and that its asymptotic distribution may or may not be normal when the error distribution is continuous. We give an exampl...

We derive the asymptotic distribution of the diaphony of n independent random variables uniformly distributed on 0; 1], describe ways to approximate its distribution function, and show an interesting relationship between this distribution, the two-sided Kolmogorov{Smirnov distribution , and the asymptotic law of the Cram er{von Mises criterion.