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

scholarly journals A Bias-Reduced Estimator for the Mean of a Heavy-Tailed Distribution with an Infinite Second Moment

2012 ◽  
Author(s):  
Brahim Brahimi ◽  
Djamel Meraghni ◽  
Necir Abdelhakim ◽  
Yahia Djabrane
Keyword(s):  
Second Moment ◽  
Heavy Tailed Distribution ◽  
The Mean ◽  
Heavy Tailed

scholarly journals A bias-reduced estimator for the mean of a heavy-tailed distribution with an infinite second moment

2013 ◽  
Vol 143 (6) ◽  
pp. 1064-1081 ◽  
Author(s):  
Brahim Brahimi ◽  
Djamel Meraghni ◽  
Abdelhakim Necir ◽  
Djabrane Yahia
Keyword(s):  
Second Moment ◽  
Heavy Tailed Distribution ◽  
The Mean ◽  
Heavy Tailed

ROBUST INFERENCE FOR THE MEAN IN THE PRESENCE OF SERIAL CORRELATION AND HEAVY-TAILED DISTRIBUTIONS

2002 ◽  
Vol 18 (5) ◽  
pp. 1019-1039 ◽  
Author(s):  
Tucker McElroy ◽  
Dimitris N. Politis
Keyword(s):  
Serial Correlation ◽  
Heavy Tails ◽  
The Self ◽  
Finite Sample ◽  
Regular Case ◽  
Sample Mean ◽  
Heavy Tailed Distributions ◽  
The Mean ◽  
Heavy Tailed ◽  
Finite Sample Simulations

The problem of statistical inference for the mean of a time series with possibly heavy tails is considered. We first show that the self-normalized sample mean has a well-defined asymptotic distribution. Subsampling theory is then used to develop asymptotically correct confidence intervals for the mean without knowledge (or explicit estimation) either of the dependence characteristics, or of the tail index. Using a symmetrization technique, we also construct a distribution estimator that combines robustness and accuracy: it is higher-order accurate in the regular case, while remaining consistent in the heavy tailed case. Some finite-sample simulations confirm the practicality of the proposed methods.

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 A Semi-Markov Leaky Integrate-and-Fire Model

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1022
Author(s):  
Giacomo Ascione ◽  
Bruno Toaldo
Keyword(s):  
Markov Process ◽  
Waiting Times ◽  
Markov Property ◽  
Fire Model ◽  
Integrate And Fire ◽  
Heavy Tailed Distribution ◽  
Semi Markov Process ◽  
The Mean ◽  
Heavy Tailed ◽  
Mean Variance

In this paper, a Leaky Integrate-and-Fire (LIF) model for the membrane potential of a neuron is considered, in case the potential process is a semi-Markov process. Semi-Markov property is obtained here by means of the time-change of a Gauss-Markov process. This model has some merits, including heavy-tailed distribution of the waiting times between spikes. This and other properties of the process, such as the mean, variance and autocovariance, are discussed.

scholarly journals Preliminary Simulation Study of Carotid Artery and Pharyngeal Constrictor Muscle Sparing-Radiotherapy in Glottic Carcinoma

2020 ◽  
Vol 19 ◽  
pp. 153303382095698
Author(s):  
Yurday Ozdemir ◽  
Ibrahim Acibuci ◽  
Ugur Selek ◽  
Erkan Topkan
Keyword(s):  
Simulation Study ◽  
Intensity Modulated Radiotherapy ◽  
Conformal Radiotherapy ◽  
Target Volume ◽  
Glottic Carcinoma ◽  
3 Dimensional ◽  
Constrictor Muscle ◽  
The Mean ◽  
The Right ◽  
3D Crt

Background: This preliminary simulation study aimed to compare the dosimetric outcomes of carotid arteries (CAs) and pharyngeal constrictor muscle (PCM) in patients with T1N0M0 glottic carcinoma undergoing helical tomotherapy-intensity modulated radiotherapy (HT-IMRT) and 3-dimensional conformal radiotherapy (3D-CRT) plans. Methods: In addition to the clinical target volume (CTV) which was defined as the entire larynx, the CAs and PCM of 11 glottic carcinoma patients were delineated. The CTV was uniformly expanded 5 mm to create a planning target volume (PTV) relative to the PCM and at a distance of 2 mm from the CA. The dosimetric characteristics in HT-IMRT and lateral opposed fields-based 3D-CRT plans were analyzed. Results: Median D95%and V100% of PTV were significantly higher in HT-IMRT (p < 0.001) compared to 3D-CRT. The right/left CA dosimetric outcomes, including the mean doses (20.7/21.5 Gy versus 48.7/50.5 Gy), Dmax (53.6/52.0 Gy versus 67.4/67.7 Gy), V30 (25.0/27.1% versus 77.6/80.3%), V40 (8.0/7.9% versus 74.6/71.9%), and V50 (2.0/1.2% versus 70.0/71.6%) were also significantly lower in HT-IMRT (p < 0.05), similar to the mean PCM doses (49.6 Gy versus 62.6 Gy for 3D-CRT;p < 0.001), respectively. Conclusions: Our present results demonstrated the feasibility of simultaneous sparing of the CAs and PCM in HT-IMRT- compared to 3D-CRT plans in glottic carcinoma patients undergoing definitive radiotherapy.

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.

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