Topic
Asymptotology
About: Asymptotology is a research topic. Over the lifetime, 1319 publications have been published within this topic receiving 35831 citations.
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TL;DR: Equations for the Edgeworth expansion of the distributions of the estimators in exploratory factor analysis and structural equation modeling and results show that asymptotic expansion gives substantial improvement of approximation to the exact distribution constructed by simulations over the usual normal approximation.
Abstract: Equations for the Edgeworth expansion of the distributions of the estimators in exploratory factor analysis and structural equation modeling are given. The equations cover the cases of non-normal data, as well as normal ones with and without known first-order asymptotic standard errors. When the standard errors are unknown, the distributions of the Studentized statistics are expanded. Methods of constructing confidence intervals of population parameters with arbitrary asymptotic confidence coefficients are given using the Cornish-Fisher expansion. Simulations are performed to see the usefulness of the asymptotic expansions in exploratory factor analysis with rotated solutions and confirmatory factor analysis. The results show that asymptotic expansion gives substantial improvement of approximation to the exact distribution constructed by simulations over the usual normal approximation.
19 citations
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19 citations
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TL;DR: In this article, asymptotic behavior of a class of fourth-order neutral delay dynamic equations with a noncanonical operator on an arbitrary time scale is studied, and an illustrative example is provided.
Abstract: This paper is concerned with asymptotic behavior of a class of fourth-order neutral delay dynamic equations with a noncanonical operator on an arbitrary time scale. A new asymptotic criterion and an illustrative example are included.
19 citations
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TL;DR: In this article, the asymptotic behavior of both the physical and unphysical metric is obtained in a Bondi-type coordinate system, and the assumptions made in this paper and the resultant metrics are compared with those of Persides in his recent paper.
Abstract: Starting with a few basic assumptions on the local asymptotic behavior of space-time and using Penrose's conformal technique the asymptotic behavior of both the physical and unphysical metric is obtained in a Bondi-type coordinate system. The space-times under consideration are not necessarily empty in the asymptotic region nor are they necessarily asymptotically flat. However, they do have the usual “falloff” behavior as one goes out toward infinity in a given null direction. The assumptions made in this paper and the resultant metrics are compared with those of Persides in his recent paper on the definition of asymptotic flatness.
19 citations
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04 Jun 2015
TL;DR: Asymptotic estimates for ODEs with turning points have been studied in this paper, where the authors show that the integration of nonlinear ODE's can be achieved by regular perturbation.
Abstract: Asymptotic Estimates.- Asymptotic Estimates for Integrals.- Regular Perturbation of ODE's.- Singularly Perturbed Linear ODE's.- Linear ODE's with Turning Points.- Asymptotic Integration of Nonlinear ODE's.- Bibliography.- Index.
18 citations