Bias reduced tail estimation for censored Pareto type distributions

2016 ◽  
Vol 109 ◽  
pp. 78-88 ◽  
Author(s):  
J. Beirlant ◽  
A. Bardoutsos ◽  
T. de Wet ◽  
I. Gijbels
Keyword(s):  
Tail Estimation ◽  
Pareto Type Distributions

scholarly journals Tail Estimation for Window-Censored Processes

Technometrics ◽  
2016 ◽  
Vol 58 (1) ◽  
pp. 95-103 ◽  
Author(s):  
Holger Rootzén ◽  
Dmitrii Zholud
Keyword(s):  
Tail Estimation

scholarly journals Extended generalised Pareto models for tail estimation

2013 ◽  
Vol 143 (1) ◽  
pp. 131-143 ◽  
Author(s):  
Ioannis Papastathopoulos ◽  
Jonathan A. Tawn
Keyword(s):  
Tail Estimation

scholarly journals Optimal heavy tail estimation – Part 1: Order selection

2017 ◽  
Vol 24 (4) ◽  
pp. 737-744 ◽  
Author(s):  
Manfred Mudelsee ◽  
Miguel A. Bermejo
Keyword(s):  
Time Series ◽  
Heavy Tails ◽  
Characteristic Exponent ◽  
Tail Probability ◽  
Heavy Tail ◽  
Infinite Variance ◽  
Accurate Estimation ◽  
Monte Carlo Experiment ◽  
River Elbe ◽  
Tail Estimation

Abstract. The tail probability, P, of the distribution of a variable is important for risk analysis of extremes. Many variables in complex geophysical systems show heavy tails, where P decreases with the value, x, of a variable as a power law with a characteristic exponent, α. Accurate estimation of α on the basis of data is currently hindered by the problem of the selection of the order, that is, the number of largest x values to utilize for the estimation. This paper presents a new, widely applicable, data-adaptive order selector, which is based on computer simulations and brute force search. It is the first in a set of papers on optimal heavy tail estimation. The new selector outperforms competitors in a Monte Carlo experiment, where simulated data are generated from stable distributions and AR(1) serial dependence. We calculate error bars for the estimated α by means of simulations. We illustrate the method on an artificial time series. We apply it to an observed, hydrological time series from the River Elbe and find an estimated characteristic exponent of 1.48 ± 0.13. This result indicates finite mean but infinite variance of the statistical distribution of river runoff.

Tail Estimation

2016 ◽  
pp. 285-290
Author(s):  
Heinz J. Klemmt ◽  
Michael Radtke ◽  
Anja Schnaus
Keyword(s):  
Tail Estimation

Large deviations of tail estimators based on the Pareto approximation

1987 ◽  
Vol 24 (03) ◽  
pp. 619-630 ◽  
Author(s):  
Richard L. Smith ◽  
Ishay Weissman
Keyword(s):  
Large Deviations ◽  
Recent Work ◽  
Relative Error ◽  
Extreme Value Theory ◽  
Value Theory ◽  
Extreme Value ◽  
Domains Of Attraction ◽  
Tail Estimation ◽  
Tail Function ◽  
General Conditions

We consider the relative error of a tail function when this is approximated by y–α using an estimator of Hill's for α. The results combine recent work of Davis and Resnick on tail estimation with Anderson's work on large deviations in extreme-value theory. Treating separately the domains of attraction of Φα and Λ, we obtain general conditions for the relative error to tend to 0 as u →∞, y → ∞ simultaneously. The results serve as warning against the automatic extrapolation of estimates based on extreme-value approximations.

scholarly journals Bivariate tail estimation: dependence in asymptotic independence

Bernoulli ◽  
2004 ◽  
Vol 10 (2) ◽  
pp. 251-280 ◽  
Author(s):  
Gerrit Draisma ◽  
Holger Drees ◽  
Ana Ferreira ◽  
Laurens De Haan
Keyword(s):  
Asymptotic Independence ◽  
Tail Estimation
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