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Showing papers on "Asymptotology published in 1985"


Journal ArticleDOI
TL;DR: In this paper, the authors consider the case where the population value of the parameter vector is a boundary point of the feasible region and show that the asymptotic distribution of test statistic is a mixture of chi-squared distributions.
Abstract: SUMMARY The analysis of moment structural models has become an important tool of investigation in behavioural, educational and economic studies. The chi-squared largesample test is routinely employed to assess the goodness of fit of the model considered. However, in order to invoke the standard asymptotic distribution theory certain regularity conditions have to be met. Here we consider the case where the population value of the parameter vector is a boundary point of the feasible region. We show that in this case the asymptotic distribution of test statistic is a mixture of chi-squared distributions. The problem of finding the corresponding weights is discussed.

269 citations


Journal ArticleDOI
TL;DR: In this paper, it was shown that the amplitude transformation of the wave equation is related to the Legendre transform of Ziolkowski and Deschamps, which is known as the asymptotic Fourier transform.
Abstract: Summary. Familiar concepts such as asymptotic ray theory and geometrical spreading are now recognized as an asymptotic form of a more general asymptotic solution to the non-separable wave equation. In seismology, the name Maslov asymptotic theory has been attached to this solution. In its simplest form, it may be thought of as a justification of disc-ray theory and it can be reduced to the WKBJ seismogram. It is a uniformly valid asymptotic solution, though. The method involves properties of the wavefronts and ray paths of the wave equation which have been established for over a century. The integral operators which build on these properties have been investigated only comparatively recently. These operators are introduced very simply by appealing to the asymptotic Fourier transform of Ziolkowski & Deschamps. This leads quite naturally to the result that phase functions in different domains of the spatial Fourier transform are related by a Legendre transformation. The amplitude transformation can also be inferred by this method. Liouville's theorem (the incompressibility of a phase space of position and slowness) ensures that it is always possible to obtain a uniformly asymptotic solution. This theorem can be derived by methods familiar to seismologists and which do not rely on the traditional formalism of classical mechanics. It can also be derived from the sympletic property of the equations of geometrical spreading and canonical transformations in general. The symplectic property plays a central role in the theory of high-frequency beams in inhomogeneous media.

95 citations


Journal ArticleDOI
TL;DR: In this paper, a general family of asymptotic solutions to Einstein's equation are presented, all of which satisfy the peeling theorem but do not satisfy the full peeling property.
Abstract: We present a general family of asymptotic solutions to Einstein's equation which are asymptotically flat but do not satisfy the peeling theorem. Near scri, the Weyl tensor obeys a logarithmic asymptotic flatness condition and has a partial peeling property. The physical significance of this asymptotic behavior arises from a quasi-Newtonian treatment of the radiation from a collapsing dust cloud. Practically all the scri formalism carries over intact to this new version of asymptotic flatness.

66 citations


Book ChapterDOI
01 Jan 1985
TL;DR: In this paper, a higher-order asymptotic theory of estimation is presented in the framework of the geometry of the model M and the ancillary family A associated with the estimator.
Abstract: A higher-order asymptotic theory of estimation is presented in this Chapter in the framework of the geometry of the model M and the ancillary family A associated with the estimator. Conditions for the consistency and efficiency of an estimator are given in geometrical terms of A. The higher-order terms of the covariance of an efficient estimators are decomposed into the sum of three non-negative geometrical terms. This proves that the bias corrected maximum likelihood estimator is the best estimator from the point of view of the third order asymptotic evaluation. The effect of parametrization is elucidated from the geometrical viewpoint.

64 citations


Journal ArticleDOI
TL;DR: For the multivariate linear model, coordinatewise M-estimators as well as an extension of the Maronna-type M estimators are considered in this article, based on the Jureckova (asymptotic) linearity of M-statistics.

41 citations


Journal ArticleDOI
TL;DR: In this article, the asymptotic estimate for large solutions of one-dimensional generalized diffusion equations with regularly varying Green functions was given for all solutions of the semigroup T_tf(x) with speed measure functions.
Abstract: We give the asymptotic estimate for large $t$ of elementary solutions of one-dimensional generalized diffusion equations with regularly varying Green functions. As a corollary we obtain the precise asymptotic behavior of the semigroup $T_tf(x)$ for all $f \in L_1(dm)$ if the speed measure function $m(x)$ is regularly varying as $x \rightarrow \pm \infty$.

19 citations


Journal ArticleDOI
TL;DR: In this paper, sufficient conditions for the uniform global asymptotic stability of the zero solution of (1.1) were given, and sufficient conditions were also given for the stability of (2.
Abstract: In this paper sufficient conditions for the uniform global asymptotic stability of the zero solution of (1.1) are given.

13 citations


Journal ArticleDOI
TL;DR: In this paper, the authors give a rigorous justification of the asymptotic expansion of Green's function for the diffraction problem on a smooth convex contour in the shadow zone.
Abstract: In the paper we give a rigorous justification of the asymptotic expansion of Green's function for the diffraction problem on a smooth convex contour γ in the shadow zone. We assume that one of the source and observation points is on the boundary γ and the other one outside γ. We consider the case of the Dirichlet problem.

11 citations




Journal ArticleDOI
TL;DR: In this article, an asymptotic decomposition technique for 2 by 2 first order singularly perturbed linear differential systems was developed and used for multi-turning point problems.
Abstract: An asymptotic decomposition technique is developed. It is designed and used for 2 by 2 first order singularly perturbed linear differential systems. A new set of decoupled linear integral equations is introduced in the process of the asymptotic analysis. Its usefulness is demonstrated with multi-turning point problems. An adiabatic theorem in quantum mechanics is proved in a general case of degenerate energy levels.


Journal ArticleDOI
TL;DR: In this article, an asymptotic theory for general statistical functional which includes L-estimators, M-estIMators, and R-stimators as special cases is developed.
Abstract: In this paper an asymptotic theory is developed for a general statistical functional which includesL-estimators,M-estimators, andR-estimators as special cases. It is shown that a proof of the asymptotic normality ofL-estimators,M-estimators, andR-estimators can be based on one important fact, namely, that the inverse c.d.f. is compactly differentiable.


Journal ArticleDOI
TL;DR: The plane-wave asymptotic expansion of the wave function for two electrons in a Coulomb field has been investigated in the case when the total orbital momentum, L, is equal to zero as mentioned in this paper.
Abstract: The plane-wave asymptotic expansion of the wavefunction for two electrons in a Coulomb field has been investigated in the case when the total orbital momentum, L, is equal to zero Analytic solutions are obtained for the first term of the asymptotic expansion The second term is found by numerical integration along classical trajectories Analytic solutions are obtained for the the Altick (1982-3) asymptotic equations It is shown that the Altick asymptotic form represents the asymptotic expression of the authors' asymptotic form The branch point of the later Altick asymptotic form has been discussed and the conclusion is made that this asymptotic form cannot be applied




01 Apr 1985
TL;DR: In this paper, the optimal control of composite materials or perforated materials is discussed and an asymptotic formula derived from the homogenization theory is presented which allows the replacement of very complicated problems by much simpler ones.
Abstract: The optimal control of structures which consist of composite materials or of perforated materials is discussed. Asymptotic formula, derived from the so-called homogenization theory, are presented which allow the replacement of very complicated problems by much simpler ones.