scholarly journals Functional kernel estimation of the conditional extreme value index under random right censoring

2021 ◽  
Vol 16 (2) ◽  
pp. 4647-2688
Author(s):  
Justin Ushize Rutikanga ◽  
Aliou Diop
Keyword(s):  
Dimensional Space ◽  
Kernel Estimation ◽  
Extreme Value ◽  
Right Censoring ◽  
Extreme Value Index ◽  
Finite Sample ◽  
Infinite Dimensional ◽  
Heavy Tailed Distribution ◽  
Weighted Kernel ◽  
Heavy Tailed

Estimation of the extreme-value index of a heavy-tailed distribution is investigated when some functional random covariate (i.e. valued in some infinite dimensional space) information is available and the scalar response variable is right-censored. A weighted kernel version of Hill’s estimator of the extreme-value index is proposed and its asymptotic normality is established under mild assumptions.A simulation study is conducted to assess the finite-sample behavior of the proposed estimator. An application to ambulatory blood pressure trajectories and clinical outcome in stroke patients is also provided.

scholarly journals Estimation of the tail-index in a conditional location-scale family of heavy-tailed distributions

2019 ◽  
Vol 7 (1) ◽  
pp. 394-417
Author(s):  
Aboubacrène Ag Ahmad ◽  
El Hadji Deme ◽  
Aliou Diop ◽  
Stéphane Girard
Keyword(s):  
Asymptotic Properties ◽  
Real Data ◽  
Scale Model ◽  
Extreme Value Index ◽  
Finite Sample ◽  
Scale Functions ◽  
Nonparametric Estimators ◽  
Heavy Tailed Distributions ◽  
Finite Sample Properties ◽  
Heavy Tailed

AbstractWe introduce a location-scale model for conditional heavy-tailed distributions when the covariate is deterministic. First, nonparametric estimators of the location and scale functions are introduced. Second, an estimator of the conditional extreme-value index is derived. The asymptotic properties of the estimators are established under mild assumptions and their finite sample properties are illustrated both on simulated and real data.

scholarly journals An Extreme Value Bayesian Lasso for the Conditional Left and Right Tails

2021 ◽  
Author(s):  
M. de Carvalho ◽  
S. Pereira ◽  
P. Pereira ◽  
P. de Zea Bermudez
Keyword(s):  
Extreme Rainfall ◽  
Value Theory ◽  
Extreme Value ◽  
Finite Sample ◽  
Bayesian Lasso ◽  
Proposed Model ◽  
Left And Right ◽  
Heavy Tailed ◽  
The Right ◽  
Type Specification

AbstractWe introduce a novel regression model for the conditional left and right tail of a possibly heavy-tailed response. The proposed model can be used to learn the effect of covariates on an extreme value setting via a Lasso-type specification based on a Lagrangian restriction. Our model can be used to track if some covariates are significant for the lower values, but not for the (right) tail—and vice versa; in addition to this, the proposed model bypasses the need for conditional threshold selection in an extreme value theory framework. We assess the finite-sample performance of the proposed methods through a simulation study that reveals that our method recovers the true conditional distribution over a variety of simulation scenarios, along with being accurate on variable selection. Rainfall data are used to showcase how the proposed method can learn to distinguish between key drivers of moderate rainfall, against those of extreme rainfall. Supplementary materials accompanying this paper appear online.

scholarly journals Estimating the Mean of Heavy-tailed Distribution under Random Truncation

2021 ◽  
pp. 273-286
Author(s):  
Ben Dahmane Khanssa
Keyword(s):  
Asymptotic Normality ◽  
Simulation Study ◽  
Random Variable ◽  
Finite Sample ◽  
Heavy Tailed Distribution ◽  
The Mean ◽  
Heavy Tailed ◽  
Alternative Estimator ◽  
The Right ◽  
Random Truncation

Inspired by L.Peng’s work on estimating the mean of heavy-tailed distribution in the case of completed data. we propose an alternative estimator and study its asymptotic normality when it comes to the right truncated random variable. A simulation study is executed to evaluate the finite sample behavior on the proposed estimator

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