The author obtains the rate of strong convergence,mean squared error and optimal choice of the“smoothing parameter”(the sample fraction)of a tail index estimator which was proposed by the author from Pickands’estim...The author obtains the rate of strong convergence,mean squared error and optimal choice of the“smoothing parameter”(the sample fraction)of a tail index estimator which was proposed by the author from Pickands’estimator,and called modified Pickands’estimator.The similar results about Hill’s estimator are also obtained,which generalize the corresponding results in.Besides,some comparisons between Hill’s estimator and the modified Pickands’estimator are given.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
We consider the random difference equations S =_d(X + S)Y and T =_dX + TY, where =_ddenotes equality in distribution, X and Y are two nonnegative random variables, and S and T on the right hand side are independent of...We consider the random difference equations S =_d(X + S)Y and T =_dX + TY, where =_ddenotes equality in distribution, X and Y are two nonnegative random variables, and S and T on the right hand side are independent of(X, Y). Under the assumptions that X follows a subexponential distribution with a nonzero lower Karamata index, that Y takes values in [0, 1] and is not degenerate at 0 or 1, and that(X, Y) fulfills a certain dependence structure via the conditional tail probability of X given Y, we derive some asymptotic formulas for the tail probabilities of the weak solutions S and T to these equations. In doing so we also obtain some by products which are interesting in their own right.展开更多
文摘通过个例总结和大样本分析的方法,本文分析和总结了ECMWF集合预报系统(EPS)中的极端温度和降水预报产品。以上产品主要为08—08时的平均气温、最高气温、最低气温和降水量四个要素的极端天气预报指数(extreme forecast index,EFI)和SOT("shift of tail"index)。研究显示,气温EFI和SOT预报效果接近,降水SOT优于EFI。运用过去3年的资料,以TS评分最大为标准,分别确定了不同时效、不同百分位的极端高低温和极端强降水事件在我国的预报阈值,及其对应的各检验参数。对于1%(99%)百分位的极端低温(高温)事件,平均气温EFI和SOT的阈值分别在-0.85(0.75)和0.38(0),最高和最低气温的阈值与平均气温的阈值接近。对于95%和99%的极端强降水事件,EFI的阈值分别在0.45和0.7左右,SOT的阈值分别在-0.6和0.4左右。整体上呈现时效越长阈值越小,预报效果越差;事件越极端,阈值越大的特点。且此时的bias接近或略大于1,表明预报的发生频率与实况比较接近,具有较好的应用价值。气温EFI和SOT的预报效果和阈值存在明显的季节差异,夏季预报较好,阈值较大,冬季预报较差,阈值较小。降水的季节差异不明显。EFI和SOT的预报效果和阈值在空间分布上也存在一定的差异,且不同的产品空间分布差异不同。
文摘The author obtains the rate of strong convergence,mean squared error and optimal choice of the“smoothing parameter”(the sample fraction)of a tail index estimator which was proposed by the author from Pickands’estimator,and called modified Pickands’estimator.The similar results about Hill’s estimator are also obtained,which generalize the corresponding results in.Besides,some comparisons between Hill’s estimator and the modified Pickands’estimator are given.
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.
基金supported by the National Science Foundation of the United States (Grant No. CMMI-1435864)
文摘We consider the random difference equations S =_d(X + S)Y and T =_dX + TY, where =_ddenotes equality in distribution, X and Y are two nonnegative random variables, and S and T on the right hand side are independent of(X, Y). Under the assumptions that X follows a subexponential distribution with a nonzero lower Karamata index, that Y takes values in [0, 1] and is not degenerate at 0 or 1, and that(X, Y) fulfills a certain dependence structure via the conditional tail probability of X given Y, we derive some asymptotic formulas for the tail probabilities of the weak solutions S and T to these equations. In doing so we also obtain some by products which are interesting in their own right.
