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Showing papers on "Asymptotology published in 1977"


Journal ArticleDOI
TL;DR: In this article, the asymptotic consistency of cross-validatory assessment and the efficiency of crossvalidatory choice is investigated both in some generality and also in the context of particular applications.
Abstract: SUMMARY The asymptotic consistency of cross-validatory assessment and the asymptotic efficiency of cross-validatory choice is investigated both in some generality and also in the context of particular applications.

289 citations


Journal ArticleDOI
TL;DR: In this article, the authors give a simple characterization of the uniform asymptotic stability of equations in terms of Lyapunov functions and a new sufficient condition is given for uniform stability.
Abstract: In this paper we give a simple characterization of the uniform asymptotic stability of equations $\dot x = - P(t)x$ where $P(t)$ is a bounded piecewise continuous symmetric positive semi-definite matrix. In the course of developing this characterization, a new and general sufficient condition is given for uniform asymptotic stability in terms of Lyapunov functions. The stability of this type of equation has come up in various control theory contexts (identification, optimization and filtering).

233 citations



Journal ArticleDOI
TL;DR: In this paper, the authors extend Sargan's approximation theorem to include non-random exogenous variables and show that valid Edgeworth expansions can be obtained in more general models.
Abstract: THERE HAS RECENTLY BEEN A GROWING INTEREST in the use of asymptotic series expansions of the Edgeworth type to approximate finite sample distributions in econometrics. Working in the framework of a conventional simultaneous equations model, a number of authors [1, 2, 6, 7, and 13] have derived such expansions for various single-equation estimators and Sargan [10] has considered the problem of developing an expansion of the distribution of the full information maximum likelihood estimator (FIML). In addition, Sargan [11] has recently established an important general theorem on the validity of Edgeworth expansions for sample distributions of statistics which can be represented as very general functions of sample data, imposing only weak conditions on the class of functions. This result covers a wide variety of econometric estimators and test statistics. Nevertheless, work in this field to date has been based on two limiting assumptions: normally distributed structural disturbances and nonrandom exogenous variables. The latter is particularly unfortunate since models in practice usually involve lagged variables in the regressor set. On the other hand, there is no reason in principle, at least, why valid expansions cannot be obtained in more general models. The present paper, therefore, is concerned with extending Sargan's approximation theorem in [11] to include such cases. The central result of the paper is stated and proved in Section 2. In Section 3 we provide some discussion of the theorem and its conditions and attempt to relate them to the contemporaneous work of Sargan in [12].

90 citations





Journal ArticleDOI
TL;DR: In this article, a systematic comparison of the time-dependent and time-independent approaches to the asymptotic analysis of some operator evolution equations in the weak or singular coupling limits is presented.

14 citations





Journal ArticleDOI
TL;DR: In this article, the asymptotic behavior of symmetric hyperbolic systems of first order with constant coefficients was studied from the point of view of L 2-theory.
Abstract: This paper studies from the view point of L 2-theory the asymptotic behavior for £-»oo of solutions (with finite energy) of symmetric hyperbolic systems of first order with constant coefficients. For each solution of such systems the corresponding asymptotic wave function will be constructed from the initial data. The asymptotic energy distributions of the solutions will be investigated making use of the asymptotic wave functions. Wilcox [8] studied these problems for solutions of the wave equation

Journal ArticleDOI
TL;DR: In this paper, the canonical operator method is used for constructing the asymptotic behavior with respect to a complex parameter of the fundamental solution of a second-order elliptic equation with smooth finite coefficients.
Abstract: Maslov's canonical operator method is used for constructing the asymptotic behavior with respect to a complex parameter of the fundamental solution of a secondorder elliptic equation with smooth finite coefficients. The asymptotic form is constructed on the assumption that all trajectories of the corresponding Hamiltonian system depart to infinity. The asymptotic form is used for investigating the analytic properties of the fundamental solution.

Journal ArticleDOI
TL;DR: A simple algorithm produces asymptotic approximations to Laplace integrals which are of higher order than those obtained by direct application of Watson's lemma.
Abstract: A simple algorithm produces asymptotic approximations to Laplace integrals which are of higher order than those obtained by direct application of Watson's lemma.

Journal ArticleDOI
TL;DR: In this paper, it was shown that the asymptotic solution of a problem of the nonlinear theory of thermoviscoelasticity, if it exists, can be found directly from the solution of the boundary value problem without completely solving the starting problem.
Abstract: It is shown that the asymptotic solution of a problem of the nonlinear theory of thermoviscoelasticity, if it exists, can be found directly from the solution of the asymptotic boundary-value problem without completely solving the starting problem.