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 Oct 1950
Abstract: Due to the asymmetry introduced by the hypothesis (2), the above theorem leaves open the case where ß >ct. Actually, the entire theorem as it stands holds without hypothesis (3). This results from the fact that Erdös' proof of the theorem given in [l ] uses only the condition a>ß/2. In the contrary case, 2a=/3, if we let ai be any fixed integer of A, the set {ö+cti}, b^B, has asymptotic density ß~\ta+ß/2; and the theorem follows. In this note it is proposed to give (using only hypotheses (1) and (2)) a short proof of (4) which does not however yield the more precise information concerning the sets of (5). This proof is based upon the (a, ß) hypothesis for Schnirelman density, proved in [2], [3]. If either a or ß equals 0, (4) follows trivially. Hence we may assume that both a and ß are not 0. Since a is the asymptotic density of A, given any e, a>e>0, we can find a largest integer m such that
2 citations
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01 Jan 2015TL;DR: In this paper, the authors analyze the finite-sample behavior of estimators and show that robust estimators, advertised as resistant to heavy-tailed distributions, can be themselves heavy-tail.
Abstract: The asymptotic distribution of an estimator approximates well the central part, but less accurately the tails of its true distribution. Some properties of estimators are always non-asymptotic, regardless a widely accepted view that their properties under moderate sample sizes are inherited from the asymptotic normality. Robust estimators, advertised as resistant to heavy-tailed distributions, can be themselves heavy-tailed. They are asymptotically admissible, but not finite-sample admissible for any distribution. While the asymptotic distribution of the Newton-Raphson iteration of an estimator, starting with a consistent initial estimator, coincides with that of the non-iterated estimator, its tail-behavior is determined by that of the initial estimator. Hence, before taking a recourse to the asymptotics, we should analyze the finite-sample behavior of an estimator, whenever possible. We shall try to illustrate some distinctive differences between the asymptotic and finite-sample properties of estimators, mainly of robust ones.
2 citations
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TL;DR: Asymptotic expansions for a wide class of distribution are studied in this paper, where simple method for the computation of the series coefficients i s suggested The case when regularization parameter of distribution depends on the asymptotics parameter is considered
Abstract: Asymptotic expansions for a wide class of distribution are studied Simple method for the computation of the series coefficients i s suggested The case when regularization parameter of distribution depends on the asymptotic parameter is considered
2 citations
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2 citations
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TL;DR: In this paper, asymptotic parametric estimation from a particle process of birth and death on a Brownian flow is considered. And when that law is specifically that of a Poisson random measure, the authors treat a computational formula for asymPTI including Fisher's information for the maximum-likelihood estimator.
2 citations