Results 221 to 230 of about 8,231 (239)

Almost sure convergence of the Hill estimator

Mathematical Proceedings of the Cambridge Philosophical Society, 1988
AbstractIn this note we characterize those sequencesknsuch that the Hill estimator of the tail index based on theknupper order statistics of a sample of sizenfrom a Pareto-type distribution is strongly consistent.
Deheuvels, Paul, Haeusler, Erich, Mason, David M.   +2 more
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SHIFTED HILL'S ESTIMATOR FOR HEAVY TAILS

Communications in Statistics - Simulation and Computation, 2001
Hill's estimator is a popular method for estimating the thickness of heavy tails. In this paper we modify Hill's estimator to make it shift-invariant as well as scale-invariant. The resulting shifted Hill's estimator is a more robust method of estimating tail thickness. †Partially supported by NSF-EAR grant 9980484.
Inmaculada B. Aban, Mark M. Meerschaert1†   +1 more
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Weak Convergence of the Hill Estimator Process

1994
Let X 1 X 2,…, be a sequence of nonnegative i. i. d. random variables and for each n ≥ 1 let X 1, n ≤… ≤ Xn, n denote the order statistics based on the first n of these X’s. The Hill estimator is the sum of extreme values Σi≤kn )/k n , where k n → ∞ and k/ n →0, as n→ ∞.
David M. Mason, Tatyana S. Turova
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Large deviation theorem for Hill's estimator

Acta Mathematica Sinica, 1992
Consider a sample of \(n\) i.i.d. random variables on the real line whose common distribution function \(F\) is regularly varying at infinity with unknown index of variation \(1/r\). A popular estimator of \(r\) is \textit{B. M. Hill's} estimator \(r_ n\) [Ann. Stat. 3, No.
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Asymptotic behavior of Hill's estimate and applications

Journal of Applied Probability, 1986
The problem of estimating the exponent of a stable law is receiving an increasing amount of attention because Pareto's law (or Zipf's law) describes many biological phenomena very well (see e.g. Hill (1974)). This problem was first solved by Hill (1975), who proposed an estimate, and the convergence of that estimate to some positive and finite number ...
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On the uniform consistency of the Hill estimator.

2008
We start by considering a kernel estimator g_{n,h}(t) for the regression function m_g(t):=E[g(Y)|X=t], where t is fixed and g:R->R is a measurable function with finite second moment. If h=h_n is a deterministic sequence such that h_n->0 and nh_n^d/log log n->\infty, it is well-known that g_{n,h_n}(t) estimates consistently m_g(t)f_X(t), where f_X is ...
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Bootstrapping Hill estimator and tail array sums for regularly varying time series

Bernoulli, 2021
Carsten Jentsch, Rafał Kulik
exaly  

Consistency of the Hill Estimator for Time Series Observed with Measurement Errors

Journal of Time Series Analysis, 2020
Piotr Kokoszka
exaly  

Assessing confidence intervals for the tail index by Edgeworth expansions for the Hill estimator

Bernoulli, 2007
Johan Segers
exaly  

Estimation of high conditional quantiles using the Hill estimator of the tail index

Journal of Statistical Planning and Inference, 2016
Tiejun Tong
exaly