scholarly journals Estimating the Second-Order Parameter of Regular Variation and Bias Reduction in Tail Index Estimation Under Random Truncation

2018 ◽  
Vol 13 (1) ◽  
Author(s):  
Nawel Haouas ◽  
Abdelhakim Necir ◽  
Brahim Brahimi
Keyword(s):  
Regular Variation ◽  
Order Parameter ◽  
Bias Reduction ◽  
Tail Index ◽  
Second Order ◽  
Tail Index Estimation ◽  
Index Estimation ◽  
Random Truncation ◽  
Second Order Parameter

Bias reduction of a tail index estimator through an external estimation of the second-order parameter

Statistics ◽  
2004 ◽  
Vol 38 (6) ◽  
pp. 497-510 ◽  
Author(s):  
M. Ivette Gomes ◽  
Frederico Caeiro ◽  
Fernanda Figueiredo
Keyword(s):  
Order Parameter ◽  
Bias Reduction ◽  
Tail Index ◽  
Second Order ◽  
Second Order Parameter

An Analysis of the Robust Convergent Method for a Singularly Perturbed Linear System of Reaction–Diffusion Type Having Nonsmooth Data

2021 ◽  
pp. 2150056
Author(s):  
Sheetal Chawla ◽  
Jagbir Singh ◽  
Urmil
Keyword(s):  
Uniform Convergence ◽  
Order Parameter ◽  
Source Term ◽  
Reaction Diffusion ◽  
Shishkin Mesh ◽  
Second Order ◽  
Singularly Perturbed ◽  
Diffusion Type ◽  
Bakhvalov Mesh ◽  
Second Order Parameter

In this paper, a coupled system of [Formula: see text] second-order singularly perturbed differential equations of reaction–diffusion type with discontinuous source term subject to Dirichlet boundary conditions is studied, where the diffusive term of each equation is being multiplied by the small perturbation parameters having different magnitudes and coupled through their reactive term. A discontinuity in the source term causes the appearance of interior layers on either side of the point of discontinuity in the continuous solution in addition to the boundary layer at the end points of the domain. Unlike the case of a single equation, the considered system does not obey the maximum principle. To construct a numerical method, a classical finite difference scheme is defined in conjunction with a piecewise-uniform Shishkin mesh and a graded Bakhvalov mesh. Based on Green’s function theory, it has been proved that the proposed numerical scheme leads to an almost second-order parameter-uniform convergence for the Shishkin mesh and second-order parameter-uniform convergence for the Bakhvalov mesh. Numerical experiments are presented to illustrate the theoretical findings.

scholarly journals Using a Bootstrap Method to Choose the Sample Fraction in Tail Index Estimation

2001 ◽  
Vol 76 (2) ◽  
pp. 226-248 ◽  
Author(s):  
J. Danielsson ◽  
L. de Haan ◽  
L. Peng ◽  
C.G. de Vries
Keyword(s):  
Bootstrap Method ◽  
Tail Index ◽  
Tail Index Estimation ◽  
Index Estimation ◽  
Sample Fraction

scholarly journals Can we determine what controls the spatio-temporal distribution of d-excess and <sup>17</sup>O-excess in precipitation using the LMDZ general circulation model?

2013 ◽  
Vol 9 (5) ◽  
pp. 2173-2193 ◽  
Author(s):  
C. Risi ◽  
A. Landais ◽  
R. Winkler ◽  
F. Vimeux
Keyword(s):  
General Circulation Model ◽  
Order Parameter ◽  
General Circulation ◽  
Temporal Distribution ◽  
Circulation Model ◽  
Second Order ◽  
Polar Ice ◽  
Spatio Temporal ◽  
Different Origins ◽  
Second Order Parameter

Abstract. Combined measurements of the H218O and HDO isotopic ratios in precipitation, leading to second-order parameter D-excess, have provided additional constraints on past climates compared to the H218O isotopic ratio alone. More recently, measurements of H217O have led to another second-order parameter: 17O-excess. Recent studies suggest that 17O-excess in polar ice may provide information on evaporative conditions at the moisture source. However, the processes controlling the spatio-temporal distribution of 17O-excess are still far from being fully understood. We use the isotopic general circulation model (GCM) LMDZ to better understand what controls d-excess and 17O-excess in precipitation at present-day (PD) and during the last glacial maximum (LGM). The simulation of D-excess and 17O-excess is evaluated against measurements in meteoric water, water vapor and polar ice cores. A set of sensitivity tests and diagnostics are used to quantify the relative effects of evaporative conditions (sea surface temperature and relative humidity), Rayleigh distillation, mixing between vapors from different origins, precipitation re-evaporation and supersaturation during condensation at low temperature. In LMDZ, simulations suggest that in the tropics convective processes and rain re-evaporation are important controls on precipitation D-excess and 17O-excess. In higher latitudes, the effect of distillation, mixing between vapors from different origins and supersaturation are the most important controls. For example, the lower d-excess and 17O-excess at LGM simulated at LGM are mainly due to the supersaturation effect. The effect of supersaturation is however very sensitive to a parameter whose tuning would require more measurements and laboratory experiments. Evaporative conditions had previously been suggested to be key controlling factors of d-excess and 17O-excess, but LMDZ underestimates their role. More generally, some shortcomings in the simulation of 17O-excess by LMDZ suggest that general circulation models are not yet the perfect tool to quantify with confidence all processes controlling 17O-excess.

Tail index estimation for heavy tails: accommodation of bias in the excesses over a high threshold

Extremes ◽  
2008 ◽  
Vol 11 (3) ◽  
pp. 303-328 ◽  
Author(s):  
M. Ivette Gomes ◽  
Lígia Henriques Rodrigues
Keyword(s):  
Heavy Tails ◽  
Tail Index ◽  
High Threshold ◽  
Tail Index Estimation ◽  
Index Estimation
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