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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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6 citations
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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.
6 citations
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6 citations
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6 citations
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TL;DR: The exactification of the Poincaré asymptotic expansion (PAE) of the Hankel integral is obtained, using the distributional approach of McClure & Wong, and it is found that, for half-integer orders of the Bessel function, the exactification terminates, so that it gives an exact finite sum representation of theHankel integral.
Abstract: We obtain an exactification of the Poincare asymptotic expansion (PAE) of the Hankel integral, as , using the distributional approach of McClure & Wong. We find that, for half-integer orders of the Bessel function, the exactified asymptotic series terminates, so that it gives an exact finite sum representation of the Hankel integral. For other orders, the asymptotic series does not terminate and is generally divergent, but is amenable to superasymptotic summation, i.e. by optimal truncation. For specific examples, we compare the accuracy of the optimally truncated asymptotic series owing to the McClure–Wong distributional method with owing to the Mellin–Barnes integral method. We find that the former is spectacularly more accurate than the latter, by, in some cases, more than 70 orders of magnitude for the same moderate value of b. Moreover, the exactification can lead to a resummation of the PAE when it is exact, with the resummed Poincare series exhibiting again the same spectacular accuracy. More importantly, the distributional method may yield meaningful resummations that involve scales that are not asymptotic sequences.
6 citations