Showing papers on "Asymptotology published in 1984"
Book•
01 Jan 1984
TL;DR: The Linear Model and Instrumental Variables Estimators as mentioned in this paper have been used to estimate Asymptotic Covariance Matrices, and Central Limit Theory has been applied to this problem.
Abstract: The Linear Model and Instrumental Variables Estimators. Consistency. Laws of Large Numbers. Asymptotic Normality. Central Limit Theory. Estimating Asymptotic Covariance Matrices. Functional Central Limit Theory and Applications. Directions for Further Study. Solution Set. References. Index.
1,746 citations
Journal Article•
85 citations
Book•
01 Jan 1984
TL;DR: Asymptotic developability and vanishing theorems of splitting lemmas in asymptotics were studied in this article. But they were not considered in this paper.
Abstract: General introduction.- Asymptotic developability and vanishing theorems in asymptotic analysis.- Existence theorems of asymptotic solutions and splitting lemmas.- Stokes phenomena and riemann-hilbert-birkhoff problem.- ?-poincare's lemma and ?-derham cohomology theorem.
39 citations
30 citations
18 citations
TL;DR: The asymptotic forms of bounds on the information rate ofLee-codes are derived and their relative strength is discussed and it is shown that the covering radius of Lee-codes lies asymPTotically on the Varshamov-Gilbert bound.
17 citations
TL;DR: The theory of radiative transfer in moving media in its classical field of applications is a well-developed branch of theoretical astrophysics as discussed by the authors, which has at its disposal a large selection of asymptotic, approximate, and numerical methods for solving different applied problems.
Abstract: It can be seen from the above review that the theory of radiative transfer in moving media in its classical field of applications is a well-developed branch of theoretical astrophysics. Studies i n recent years have clarified important questions such as the asymptotic behavior of the kernel functions and the characteristic lengths of the theory. It has been established that there are two types of radiative coupling, and the influence of nonlocal radiative coupling on the formation of spectral lines and radiation pressure has been investigated. The theory now has at its disposal a large selection of asymptotic, approximate, and numerical methods for solving different applied problems.
16 citations
TL;DR: In this article, four simple examples illustrating varieties of pathological asymptotic behavior are presented, which are based on some recent work on l 1Asymptotics, and have some pedagogical value in clarifying the role of certain standard regularity conditions.
Abstract: Four simple examples illustrating varieties of pathological asymptotic behavior are presented. The examples are based on some recent work on l 1 asymptotics. The examples have some pedagogical value in clarifying the role of certain standard regularity conditions.
9 citations
4 citations
01 Jan 1984
TL;DR: Boundary element methods which can be considered as numerical or finite element approximations of boundary integral equations on closed boundary manifolds became very popular during the last years and correspondingly, a great variety of boundary value problems can now be solved numerically with corresponding boundary element programs as mentioned in this paper.
Abstract: Boundary element methods which can be considered as numerical or finite element approximations of boundary integral equations on closed boundary manifolds became very popular during the last years and, correspondingly,a great variety of boundary value problems can now be solved numerically with corresponding boundary element programs. Since the reduction of interior or exterior boundary value problems and also transmission problems to equivalent boundary integral equations is by no means a uniquely determined process — even for one specific boundary value problem — the growing number of applications has led to an enormous variety of mathematical problems and questions in connection with the applicability, correctness of formulations, systematical and computational errors and their estimation, computing times and expenses and efficiency.
TL;DR: In this article, the perturbation series for the formal integral of two-dimensional area-preserving mappings is considered and asymptotic formulas for large order terms of this expansion are derived.
TL;DR: In this paper, an asymptotic version of Poincare's lemma is defined and solutions are obtained with the calculus of exterior differential forms for multidimensional oscillatory integrals whose forms are commonly encountered, for example, in electromagnetic problems.
Abstract: An asymptotic version of Poincare’s lemma is defined and solutions are obtained with the calculus of exterior differential forms. They are used to construct the asymptotic approximations of multidimensional oscillatory integrals whose forms are commonly encountered, for example, in electromagnetic problems. In particular, the boundary and stationary point evaluations of these integrals are considered. The former is applied to the Kirchhoff representation of a scalar field diffracted through an aperture and simply recovers the Maggi–Rubinowicz–Miyamoto–Wolf results. Asymptotic approximations in the presence of other (standard) critical points are also discussed. Techniques developed for the asymptotic Poincare lemma are used to generate a general representation of the Leray form. All of the (differential form) expressions presented are generalizations of known (vector calculus) results.
01 Jan 1984
TL;DR: In this paper, the authors discuss asymptotic normality, convergence in distribution, product rule, uniqueness theorem, and continuity theorem for hypothesis testing, and present the Lagrange multiplier test and the likelihood ratio test.
Abstract: Publisher Summary
This chapter discusses asymptotic normality, convergence in distribution, product rule, asymptotic equivalence, uniqueness theorem, and continuity theorem. A direct and very important use of the asymptotic normality of a given estimator is in hypothesis testing. Often, hypotheses of interest can be expressed in terms of linear combinations of the parameters. The chapter also describes the Lagrange multiplier test, mean value theorem, likelihood ratio test, and asymptotic efficiency. Given a class of estimators, it is desirable to choose that member of the class that has the smallest asymptotic covariance matrix. The reason for this is that such estimators are more precise and in general allow the construction of more powerful test statistics.
TL;DR: In this paper, the problem of finding asymptotic equivalence between two systems of ODEs has been investigated, using a variation of constants formula in conjunction with a fixed-point theorem.
TL;DR: In this article, asymptotic results in the theory of ordinary differential equations are applied to certain scalar and vector boundary value problems that model various nonlinear dissipative and dispersive wave phenomena.
01 Jan 1984