The bootstrap method is one of the new ways of studying statistical math which this article uses but is a major tool for studying and evaluating the values of parameters in probability distribution.Our research is con...The bootstrap method is one of the new ways of studying statistical math which this article uses but is a major tool for studying and evaluating the values of parameters in probability distribution.Our research is concerned overview of the theory of infinite distribution functions.The tool to deal with the problems raised in the paper is the mathematical methods of random analysis(theory of random process and multivariate statistics).In this article,we introduce the new function to find out the bias and standard error with jackknife method for Generalized Extreme Value distributions.展开更多
The exponential Randić index has important applications in the fields of biology and chemistry. The exponential Randić index of a graph G is defined as the sum of the weights e 1 d( u )d( v ) of all edges uv of G, whe...The exponential Randić index has important applications in the fields of biology and chemistry. The exponential Randić index of a graph G is defined as the sum of the weights e 1 d( u )d( v ) of all edges uv of G, where d( u ) denotes the degree of a vertex u in G. The paper mainly provides the upper and lower bounds of the exponential Randić index in quasi-tree graphs, and characterizes the extremal graphs when the bounds are achieved.展开更多
This paper investigates methods of value-at-risk (VaR) estimation using extreme value theory (EVT). It compares two different estimation methods, 'two-step subsample bootstrap' based on moment estimation and m...This paper investigates methods of value-at-risk (VaR) estimation using extreme value theory (EVT). It compares two different estimation methods, 'two-step subsample bootstrap' based on moment estimation and maximum likelihood estimation (MLE), according to their theoretical bases and computation procedures. Then, the estimation results are analyzed together with those of normal method and empirical method. The empirical research of foreign exchange data shows that the EVT methods have good characters in estimating VaR under extreme conditions and 'two-step subsample bootstrap' method is preferable to MLE.展开更多
In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order ...In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order regular variation condition.展开更多
This review paper discusses advances of statistical inference in modeling extreme observations from multiple sources and heterogeneous populations.The paper starts briefly reviewing classical univariate/multivariate e...This review paper discusses advances of statistical inference in modeling extreme observations from multiple sources and heterogeneous populations.The paper starts briefly reviewing classical univariate/multivariate extreme value theory,tail equivalence,and tail(in)dependence.New extreme value theory for heterogeneous populations is then introduced.Time series models for maxima and extreme observations are the focus of the review.These models naturally form a new system with similar structures.They can be used as alternatives to the widely used ARMA models and GARCH models.Applications of these time series models can be in many fields.The paper discusses two important applications:systematic risks and extreme co-movements/large scale contagions.展开更多
Modelling of intraday increases in peak electricity demand using an autoregressive moving average-exponential generalized autoregressive conditional heteroskedastic-generalized single Pareto (ARMA-EGARCH-GSP) approach...Modelling of intraday increases in peak electricity demand using an autoregressive moving average-exponential generalized autoregressive conditional heteroskedastic-generalized single Pareto (ARMA-EGARCH-GSP) approach is discussed in this paper. The developed model is then used for extreme tail quantile estimation using daily peak electricity demand data from South Africa for the period, years 2000 to 2011. The advantage of this modelling approach lies in its ability to capture conditional heteroskedasticity in the data through the EGARCH framework, while at the same time estimating the extreme tail quantiles through the GSP modelling framework. Empirical results show that the ARMA-EGARCH-GSP model produces more accurate estimates of extreme tails than a pure ARMA-EGARCH model.展开更多
Geostatistics of extreme values makes it possible to model the asymptotic behavior of random phenomena that depend on time or space. In this paper, we propose new models of the extremal coefficient of a stationary ran...Geostatistics of extreme values makes it possible to model the asymptotic behavior of random phenomena that depend on time or space. In this paper, we propose new models of the extremal coefficient of a stationary random field where the cumulative distribution is associated with a multivariate copula. More precisely, some models of extensions of the extremogram and these derivatives are built in a spatial framework. Moreover, both these two geostatistical tools are modeled using the extremal variogram which characterizes the asymptotic stochastic behavior of the phenomena.展开更多
Proceeded from trimmed Hill estimators and distributed inference, a new distributed version of trimmed Hill estimator for heavy tail index is proposed. Considering the case where the number of observations involved in...Proceeded from trimmed Hill estimators and distributed inference, a new distributed version of trimmed Hill estimator for heavy tail index is proposed. Considering the case where the number of observations involved in each machine can be either the same or different and either fixed or varying to the total sample size, its consistency and asymptotic normality are discussed. Simulation studies are particularized to show the new estimator performs almost in line with the trimmed Hill estimator.展开更多
Estimation of the extreme conditional quantiles with functional covariate is an important problem in quantile regression. The existing methods, however, are only applicable for heavy-tailed distributions with a positi...Estimation of the extreme conditional quantiles with functional covariate is an important problem in quantile regression. The existing methods, however, are only applicable for heavy-tailed distributions with a positive conditional tail index. In this paper, we propose a new framework for estimating the extreme conditional quantiles with functional covariate that combines the nonparametric modeling techniques and extreme value theory systematically. Our proposed method is widely applicable, no matter whether the conditional distribution of a response variable Y given a vector of functional covariates X is short, light or heavy-tailed. It thus enriches the existing literature.展开更多
文摘The bootstrap method is one of the new ways of studying statistical math which this article uses but is a major tool for studying and evaluating the values of parameters in probability distribution.Our research is concerned overview of the theory of infinite distribution functions.The tool to deal with the problems raised in the paper is the mathematical methods of random analysis(theory of random process and multivariate statistics).In this article,we introduce the new function to find out the bias and standard error with jackknife method for Generalized Extreme Value distributions.
文摘The exponential Randić index has important applications in the fields of biology and chemistry. The exponential Randić index of a graph G is defined as the sum of the weights e 1 d( u )d( v ) of all edges uv of G, where d( u ) denotes the degree of a vertex u in G. The paper mainly provides the upper and lower bounds of the exponential Randić index in quasi-tree graphs, and characterizes the extremal graphs when the bounds are achieved.
基金the National Natural Science Foundation of China (No. 79970041).
文摘This paper investigates methods of value-at-risk (VaR) estimation using extreme value theory (EVT). It compares two different estimation methods, 'two-step subsample bootstrap' based on moment estimation and maximum likelihood estimation (MLE), according to their theoretical bases and computation procedures. Then, the estimation results are analyzed together with those of normal method and empirical method. The empirical research of foreign exchange data shows that the EVT methods have good characters in estimating VaR under extreme conditions and 'two-step subsample bootstrap' method is preferable to MLE.
文摘In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order regular variation condition.
基金partially supported by NSF-DMS-1505367 and NSF-DMS-2012298.
文摘This review paper discusses advances of statistical inference in modeling extreme observations from multiple sources and heterogeneous populations.The paper starts briefly reviewing classical univariate/multivariate extreme value theory,tail equivalence,and tail(in)dependence.New extreme value theory for heterogeneous populations is then introduced.Time series models for maxima and extreme observations are the focus of the review.These models naturally form a new system with similar structures.They can be used as alternatives to the widely used ARMA models and GARCH models.Applications of these time series models can be in many fields.The paper discusses two important applications:systematic risks and extreme co-movements/large scale contagions.
文摘Modelling of intraday increases in peak electricity demand using an autoregressive moving average-exponential generalized autoregressive conditional heteroskedastic-generalized single Pareto (ARMA-EGARCH-GSP) approach is discussed in this paper. The developed model is then used for extreme tail quantile estimation using daily peak electricity demand data from South Africa for the period, years 2000 to 2011. The advantage of this modelling approach lies in its ability to capture conditional heteroskedasticity in the data through the EGARCH framework, while at the same time estimating the extreme tail quantiles through the GSP modelling framework. Empirical results show that the ARMA-EGARCH-GSP model produces more accurate estimates of extreme tails than a pure ARMA-EGARCH model.
文摘Geostatistics of extreme values makes it possible to model the asymptotic behavior of random phenomena that depend on time or space. In this paper, we propose new models of the extremal coefficient of a stationary random field where the cumulative distribution is associated with a multivariate copula. More precisely, some models of extensions of the extremogram and these derivatives are built in a spatial framework. Moreover, both these two geostatistical tools are modeled using the extremal variogram which characterizes the asymptotic stochastic behavior of the phenomena.
文摘Proceeded from trimmed Hill estimators and distributed inference, a new distributed version of trimmed Hill estimator for heavy tail index is proposed. Considering the case where the number of observations involved in each machine can be either the same or different and either fixed or varying to the total sample size, its consistency and asymptotic normality are discussed. Simulation studies are particularized to show the new estimator performs almost in line with the trimmed Hill estimator.
基金Supported by the National Natural Science Foundation of China(Grant No.11671338)the Hong Kong Baptist University(Grant Nos.FRG1/16-17/018 and FRG2/16-17/074)
文摘Estimation of the extreme conditional quantiles with functional covariate is an important problem in quantile regression. The existing methods, however, are only applicable for heavy-tailed distributions with a positive conditional tail index. In this paper, we propose a new framework for estimating the extreme conditional quantiles with functional covariate that combines the nonparametric modeling techniques and extreme value theory systematically. Our proposed method is widely applicable, no matter whether the conditional distribution of a response variable Y given a vector of functional covariates X is short, light or heavy-tailed. It thus enriches the existing literature.
