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Jean-françois Dupuy - One of the best experts on this subject based on the ideXlab platform.

  • Bayesian estimation of the tail index of a heavy tailed Distribution under random censoring
    Computational Statistics and Data Analysis, 2016
    Co-Authors: Abdelkader Ameraoui, Kamal Boukhetala, Jean-françois Dupuy
    Abstract:

    Bayesian estimation of the tail index of a Heavy-Tailed Distribution is addressed when data are randomly right-censored. Maximum a posteriori and mean posterior estimators are constructed for various prior Distributions of the tail index and their consistency and asymptotic normality are established. Finite-sample properties of the proposed estimators are investigated via simulations. Tail index estimation requires selecting an appropriate threshold for constructing relative excesses. A Monte Carlo procedure is proposed for tackling this issue. Finally, the proposed estimators are illustrated on a medical dataset.

  • Bayesian estimation of the tail index of a heavy tailed Distribution under random censoring
    Computational Statistics & Data Analysis, 2016
    Co-Authors: Abdelkader Ameraoui, Kamal Boukhetala, Jean-françois Dupuy
    Abstract:

    International audienceBayesian estimation of the tail index of a Heavy-Tailed Distribution is addressed when data are randomly right-censored. Maximum a posteriori and mean posterior estimators are constructed for various prior Distributions of the tail index and their consistency and asymptotic normality are established. Finite-sample properties of the proposed estimators are investigated via simulations. Tail index estimation requires selecting an appropriate threshold for constructing relative excesses. A Monte Carlo procedure is proposed for tackling this issue. Finally, the proposed estimators are illustrated on a medical dataset

  • Nonparametric estimation of the conditional extreme-value index with random covariates and censoring
    Journal of Statistical Planning and Inference, 2016
    Co-Authors: Pathé Ndao, Aliou Diop, Jean-françois Dupuy
    Abstract:

    Estimation of the extreme-value index of a Heavy-Tailed Distribution is addressed when some random covariate information is available and the data are randomly right-censored. An inverse-probability-of-censoring-weighted kernel version of Hill's estimator of the extreme-value index is proposed and its asymptotic normality is established. Based on this, a Weissman-type estimator of conditional extreme quantiles is also constructed. A simulation study is conducted to assess the finite-sample behaviour of the proposed estimators.

  • Nonparametric estimation of the conditional tail index and extreme quantiles under random censoring
    Computational Statistics and Data Analysis, 2014
    Co-Authors: Pathé Ndao, Aliou Diop, Jean-françois Dupuy
    Abstract:

    In this paper, we investigate the estimation of the tail index and extreme quantiles of a Heavy-Tailed Distribution when some covariate information is available and the data are randomly right-censored. We construct several estimators by combining a moving-window technique (for tackling the covariate information) and the inverse probability-of-censoring weighting method, and we establish their asymptotic normality. A comprehensive simulation study is conducted to evaluate the finite-sample performance of the proposed estimators and to identify their application scope.

Robert C. Jung - One of the best experts on this subject based on the ideXlab platform.

  • Stochastic Volatility Models: Conditional Normality Versus Heavy-Tailed Distributions
    SSRN Electronic Journal, 1997
    Co-Authors: Roman Liesenfeld, Robert C. Jung
    Abstract:

    Most of the empirical applications of the stochatic volatility (SV) model are based on the assumption that the conditional Distribution of returns given the latent volatility process is normal. In this paper the SV model based on a conditional normal Distribution is compared with SV specifications using conditional Heavy-Tailed Distributions, especially Student's t-Distribution and the generalized error Distribution. To estimate the SV specifications a simulated maximum likelihood approach is applied. The results based on German stock market data reveal that the SV model with a conditional normal Distribution does not adequately account for the two following empirical facts simultaneously: the leptokurtic Distribution of the returns and the low but slowly decaying autocorrelation functions of the squared returns. It is shown that these empirical facts are more adequately captured by a SV model with a conditional Heavy-Tailed Distribution. Finally, it turns out that the choice of the conditional Distribution has systematic effects on the parameter estimates of the volatility process.

  • Stochastic volatility models: Conditional normality versus heavy tailed Distributions
    1997
    Co-Authors: Roman Liesenfeld, Robert C. Jung
    Abstract:

    Most of the empirical applications of the stochatic volatility (SV) model are based on the assumption that the conditional Distribution of returns given the latent volatility process is normal. In this paper the SV model based on a conditional normal Distribution is compa-red with SV specifications using conditional Heavy-Tailed Distributions, especially Student's i-Distribution and the generalized error Distribution. To estimate the SV specifications a si-mulated maximum likelihood approach is applied. The results based on German stock market data reveal that the SV model with a conditional normal Distribution does not adequately account for the two following empirical facts simultaneously: the leptokurtic Distribution of the returns and low but slowly decaying autocorrelation function of the squared returns. It is shown that these empirical facts are more adequately captured by a SV model with a conditional Heavy-Tailed Distribution. Finally, it turns out that the choice of the conditional Distribution has systematic effects on the parameter estimates of the volatility process.

Yoshito Ohta - One of the best experts on this subject based on the ideXlab platform.

  • stable process approach to analysis of systems under heavy tailed noise modeling and stochastic linearization
    IEEE Transactions on Automatic Control, 2019
    Co-Authors: Kenji Kashima, Hiroki Aoyama, Yoshito Ohta
    Abstract:

    The Wiener process has provided a lot of practically useful mathematical tools to model stochastic noise in many applications. However, this framework is not enough for modeling extremal events, since many statistical properties of dynamical systems driven by the Wiener process are inevitably Gaussian. The goal of this work is to develop a framework that can represent a Heavy-Tailed Distribution without losing the advantages of the Wiener process. To this end, we investigate models based on stable processes (this term “stable” has nothing to do with “dynamical stability”) and clarify their fundamental properties. In addition, we propose a method for stochastic linearization, which enables us to approximately linearize static nonlinearities in feedback systems under Heavy-Tailed noise, and analyze the resulting error theoretically. The proposed method is applied to assessing wind power fluctuation to show the practical usefulness.

Gilles Stupfler - One of the best experts on this subject based on the ideXlab platform.

  • Extreme versions of Wang risk measures and their estimation for Heavy-Tailed Distributions
    Statistica Sinica, 2017
    Co-Authors: Jonathan El Methni, Gilles Stupfler
    Abstract:

    Among the many possible ways to study the right tail of a real-valued random variable, a particularly general one is given by considering the family of its Wang distortion risk measures. This class of risk measures encompasses various interesting indicators, such as the widely used Value-at-Risk and Tail Value-at-Risk, which are especially popular in actuarial science, for instance. In this paper, we first build simple extreme analogues of Wang distortion risk measures and we show how this makes it possible to consider many standard measures of extreme risk, including the usual extreme Value-at-Risk or Tail-Value-at-Risk, as well as the recently introduced extreme Conditional Tail Moment, in a unified framework. We then introduce adapted estimators when the random variable of interest has a Heavy-Tailed Distribution and we prove their asymptotic normality. The finite sample performance of our estimators is assessed on a simulation study and we showcase our techniques on two sets of real data.

  • Extreme versions of Wang risk measures and their estimation for Heavy-Tailed Distributions
    2016
    Co-Authors: Jonathan El Methni, Gilles Stupfler
    Abstract:

    Among the many possible ways to study the right tail of a real-valued random variable, a particularly general one is given by considering the family of its Wang distortion risk measures. This class of risk measures encompasses various interesting indicators, such as the widely used Value-at-Risk and Tail Value-at-Risk, which are especially popular in actuarial science, for instance. In this communication, we first build simple extreme analogues of Wang distortion risk measures and we show how this makes it possible to consider many standard measures of extreme risk, including the usual extreme Value-at-Risk or Tail-Value-at-Risk, as well as the recently introduced extreme Conditional Tail Moment, in a unified framework. We then introduce adapted estimators when the random variable of interest has a Heavy-Tailed Distribution and we prove their asymptotic normality. The finite sample performance of our estimators is assessed on a simulation study and we showcase our techniques on an actuarial data set.

  • Extreme versions of Wang risk measures and their estimation
    2016
    Co-Authors: Jonathan El Methni, Gilles Stupfler
    Abstract:

    Among the many possible ways to study the right tail of a real-valued random variable, a particularly general one is given by considering the family of its Wang distortion risk measures. This class of risk measures encompasses various interesting indicators, such as the widely used Value-at-Risk and Tail Value-at-Risk, which are especially popular in actuarial science, for instance. In this communication, we first build simple extreme analogues of Wang distortion risk measures and we show how this makes it possible to consider many standard measures of extreme risk, including the usual extreme Value-at-Risk or Tail-Value-at-Risk, as well as the recently in- troduced extreme Conditional Tail Moment, in a unified framework. We then introduce adapted estimators when the random variable of interest has a Heavy-Tailed Distribution and we prove their asymptotic normality. The finite sample performance of our estimators is assessed on a simulation study and we showcase our techniques on an actuarial data set.

  • Extreme versions of Wang risk measures and their estimation
    2015
    Co-Authors: Jonathan El Methni, Gilles Stupfler
    Abstract:

    Among the many possible ways to study the right tail of a real-valued random variable, a particularly general one is given by considering the family of its Wang distortion risk measures. This class of risk measures encompasses various interesting indicators such as the widely used Value-at-Risk and Tail Value-at-Risk, which are especially popular in actuarial science, for instance. We start by building simple extreme analogues of Wang distortion risk measures. Special cases of the risk measures of interest include the extreme Value-at-Risk as well as the recently introduced extreme Conditional Tail Moment. Adapted estimators of the resulting extreme Wang distortion risk measures are then introduced when the random variable of interest has a Heavy-Tailed Distribution and their asymptotic normality is shown. The finite sample performance of our estimators is assessed on a simulation study.

  • Estimating the conditional tail index with an integrated conditional log-quantile estimator in the random covariate case
    2014
    Co-Authors: Laurent Gardes, Gilles Stupfler
    Abstract:

    It is well known that the tail behavior of a Heavy-Tailed Distribution is controlled by a parameter called the tail index. Such a parameter is therefore of primary interest in extreme value analysis, particularly to estimate extreme quantiles. In various applications, the random variable of interest can be linked to a finite-dimensional random covariate. In such a situation, the tail index is function of the covariate and is referred to as the conditional tail index. The goal of this paper is to provide a class of estimators of this quantity. The pointwise weak consistency and asymptotic normality of these estimators are established. We illustrate the finite sample performance of our technique on a simulation study and on a real hurricane data set.

Roman Liesenfeld - One of the best experts on this subject based on the ideXlab platform.

  • Stochastic Volatility Models: Conditional Normality Versus Heavy-Tailed Distributions
    SSRN Electronic Journal, 1997
    Co-Authors: Roman Liesenfeld, Robert C. Jung
    Abstract:

    Most of the empirical applications of the stochatic volatility (SV) model are based on the assumption that the conditional Distribution of returns given the latent volatility process is normal. In this paper the SV model based on a conditional normal Distribution is compared with SV specifications using conditional Heavy-Tailed Distributions, especially Student's t-Distribution and the generalized error Distribution. To estimate the SV specifications a simulated maximum likelihood approach is applied. The results based on German stock market data reveal that the SV model with a conditional normal Distribution does not adequately account for the two following empirical facts simultaneously: the leptokurtic Distribution of the returns and the low but slowly decaying autocorrelation functions of the squared returns. It is shown that these empirical facts are more adequately captured by a SV model with a conditional Heavy-Tailed Distribution. Finally, it turns out that the choice of the conditional Distribution has systematic effects on the parameter estimates of the volatility process.

  • Stochastic volatility models: Conditional normality versus heavy tailed Distributions
    1997
    Co-Authors: Roman Liesenfeld, Robert C. Jung
    Abstract:

    Most of the empirical applications of the stochatic volatility (SV) model are based on the assumption that the conditional Distribution of returns given the latent volatility process is normal. In this paper the SV model based on a conditional normal Distribution is compa-red with SV specifications using conditional Heavy-Tailed Distributions, especially Student's i-Distribution and the generalized error Distribution. To estimate the SV specifications a si-mulated maximum likelihood approach is applied. The results based on German stock market data reveal that the SV model with a conditional normal Distribution does not adequately account for the two following empirical facts simultaneously: the leptokurtic Distribution of the returns and low but slowly decaying autocorrelation function of the squared returns. It is shown that these empirical facts are more adequately captured by a SV model with a conditional Heavy-Tailed Distribution. Finally, it turns out that the choice of the conditional Distribution has systematic effects on the parameter estimates of the volatility process.