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On asymptotic normality of the hill estimator [PDF]
Stochastic Models, 1998 For iid observations from a common distribution Fwith regularly varying tail , a popular estimator of α is the Hill estimator. Regular variation of the distribution tail is equivalent to weak consistency of the Hill estimator in a manner made precise in Mason (1982) but necessary and sufficient conditions for asymptotic normality of this estimator are ...
Sidney Resnick
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Penultimate Approximation for Hill's Estimator [PDF]
Scandinavian Journal of Statistics, 2001 We prove that the probability distribution of Hill's estimator can be better approximated by a series of appropriate gamma distributions than by the limiting normal distribution.
S. Cheng, L.F.M. de Haan
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Inference about the Tail of a Distribution: Improvementon the Hill Estimator [PDF]
International Journal of Mathematics and Mathematical Sciences, 2010 The Hill estimator is often used to infer the power behavior in tails of experimental distribution functions. This estimator is known to produce bad results in certain situations which have lead to the so-called Hill horror plots.
Jean Nuyts
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Asymptotic Normality of Hill Estimator for Truncated Data
Electronic Journal of Probability, 2011 The problem of estimating the tail index from truncated data is addressed in Chakrabarty and Samorodnitsky (2009). In that paper, a sample based (and hence random) choice of k is suggested, and it is shown that the choice leads to a consistent estimator of the inverse of the tail index.
Arijit Chakrabarty
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Normalising Transformation of the Hill Estimator
Australian and New Zealand Journal of StatisticsABSTRACTWe present a normalising transformation of the Hill estimator to improve the convergence rate in finite‐sample performance. Our proposal for the normalising transformation is based on the higher order asymptotic expansion of the Hill estimator. The transformation is automatic and simple in computation. The resulting transformation theoretically
Yan Liu
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Distributed Trimmed Hill Estimator
Journal of Applied Mathematics and Physics, 2023 exaly +2 more sources
Smoothing the Hill Estimator [PDF]
Advances in Applied Probability, 1997 For sequences of i.i.d. random variables whose common tail 1 –Fis regularly varying at infinity wtih an unknown index –α< 0, it is well known that the Hill estimator is consistent for α–1and usually asymptotically normally distributed. However, because the Hill estimator is a function ofk = k(n), the number of upper order statistics used and which ...
Resnick, Sidney, Stărică, Cătălin
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A class of weighted Hill estimators
Computational and Mathematical Methods, 2021 In Statistics of Extremes, the estimation of the extreme value index is an essential requirement for further tail inference. In this work, we deal with the estimation of a strictly positive extreme value index from a model with a Pareto-type right tail.
Frederico Caeiro +2 more
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Estimating and comparing microbial diversity in the presence of sequencing errors [PDF]
PeerJ, 2016 Estimating and comparing microbial diversity are statistically challenging due to limited sampling and possible sequencing errors for low-frequency counts, producing spurious singletons. The inflated singleton count seriously affects statistical analysis
Chun-Huo Chiu, Anne Chao
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Weak properties and robustness of t-Hill estimators [PDF]
Extremes, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jordanova, Pavlina +7 more
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