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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01 Dec 1986
TL;DR: Sufficient conditions for finite difference equations with a solution behaving in a precisely specified way like a given polynomial are given in this paper, and sufficient conditions for polynomials with a similar solution are also given.
Abstract: Sufficient conditions for somem-th order finite difference equations are presented which have a solution behaving in a precisely specified way like a given polynomial.
11 citations
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01 Feb 1972
TL;DR: In this article, a variation of the variation of constants formula for nonlinear systems is used to study the comparative asymptotic behavior of the systems x' = f(t, x) and y'=f(T, y)+g(t, y).
Abstract: A version of the variation of constants formula for nonlinear systems is used to study the comparative asymptotic behavior of the systems x'=f(t, x) and y'=f(t, y)+g(t, y).
11 citations
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TL;DR: The asymPTotic robustness of the normal theory asymptotic biases of the least-squares estimators of the parameters in covariance structures against the violation of normality is shown.
11 citations
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TL;DR: In this article, the authors studied the asymptotic mean squared error for predicting the integral of a weakly stationary spatial process over a unit cube based on a centered systematic sample.
Abstract: This paper studies the asymptotic mean squared error for predicting the integral of a weakly stationary spatial process over a unit cube based on a centered systematic sample. For processes whose spectral density decays sufficiently slowly at infinity, the asymptotic mean squared error takes a form similar to that obtained by letting the cube increase in size with the number of observations. However, if the spectral density decays faster than a certain critical rate, then the asymptotic mean squared error takes on a completely different form. By adjusting the weights given to observations near an edge of the cube, it is possible to obtain asymptotic results for the fixed cube that again resemble those for the increasing cube.
11 citations