论文检索

通过平均分布尾部分析一般异质数据的极值统计AI 解读

In the general setting of independent data with possibly very different distributions, extreme value estimators inevitably target the tail of the average distribution function. We consider all possible cases, that is, the extreme value index of the average distribution can be negative, zero, or positive, and we present novel asymptotic theory for the moment estimator. Our results require a different and much more challenging proof than those for the power-law case and are…

基于经验似然的多元正则变差检验AI 解读

Multivariate regular variation is a common assumption in the statistics literature and needs to be verified in real-data applications. We develop a novel hypothesis test for multivariate regular variation, employing localized empirical likelihood. We establish the weak convergence of the test statistic to a nonstandard, distribution-free limit and hence can provide universal critical values for the test. We show the very good finite-sample behavior of the procedure through…

尾部 Copula 的双样本检验及股票指数应用AI 解读

A novel, general two-sample hypothesis testing procedure is established for testing the equality of tail copulas associated with bivariate data.More precisely, using a martingale transformation of a natural twosample tail copula process, a test process is constructed, which is shown to converge in distribution to a standard Wiener process.Hence, from this test process a myriad of asymptotically distribution-free twosample tests can be obtained.The good finite-sample behavior…

异质数据的极值估计AI 解读

We develop a universal econometric formulation of empirical power laws possibly driven by parameter heterogeneity. Our approach extends classical extreme value theory to specifying the tail behavior of the empirical distribution of a general dataset with possibly heterogeneous marginal distributions. We discuss several model examples that satisfy our conditions and demonstrate in simulations how heterogeneity may generate empirical power laws. We observe a cross-sectional…

密度水平集经验估计量的立方根弱收敛AI 解读

Given n independent random vectors with common density f on Rd, we study the weak convergence of three empirical-measure based estimators of the convex λ-level set Lλ of f, namely the excess mass set, the minimum volume set and the maximum probability set, all selected from a class of convex sets A that contains Lλ. Since these set-valued estimators approach Lλ, even the formulation of their weak convergence is nonstandard. We identify the joint limiting distribution of the…

极端事件的空间依赖与时空趋势AI 解读

The statistical theory of extremes is extended to independent multivariate observations that are non-stationary both over time and across space. The non-stationarity over time and space is controlled via the scedasis (tail scale) in the marginal distributions. Spatial dependence stems from multivariate extreme value theory. We establish asymptotic theory for both the weighted sequential tail empirical process and the weighted tail quantile process based on all observations,…

多元正则变差模型的检验AI 解读

In this article, we propose a test for the multivariate regular variation (MRV) model. The test is based on testing whether the extreme value indices of the radial component conditional on the angular component falling in different subsets are the same. Combining the test on the constancy across extreme value indices in different directions with testing the regular variation of the radial component, we obtain the test for testing MRV. Simulation studies demonstrate the good…

函数型数据的经验尾部 CopulaAI 解读

For multivariate distributions in the domain of attraction of a max-stable distribution, the tail copula and the stable tail dependence function are equivalent ways to capture the dependence in the upper tail. The empirical versions of these functions are rank-based estimators whose inflated estimation errors are known to converge weakly to a Gaussian process that is similar in structure to the weak limit of the empirical copula process. We extend this multivariate result to…

基于深度的极端分位数区域估计AI 解读

Summary Consider the extreme quantile region induced by the half-space depth function HD of the form Q={x∈Rd:HD(x,P)⩽β}, such that PQ=p for a given, very small p > 0. Since this involves extrapolation outside the data cloud, this region can hardly be estimated through a fully non-parametric procedure. Using extreme value theory we construct a natural semiparametric estimator of this quantile region and prove a refined consistency result. A simulation study clearly…

空间尾部依赖的 M 估计量AI 解读

Summary Tail dependence models for distributions attracted to a max-stable law are fitted by using observations above a high threshold. To cope with spatial, high dimensional data, a rank-based M-estimator is proposed relying on bivariate margins only. A data-driven weight matrix is used to minimize the asymptotic variance. Empirical process arguments show that the estimator is consistent and asymptotically normal. Its finite sample performance is assessed in simulation…

异方差极端值的统计分析AI 解读

Summary We extend classical extreme value theory to non-identically distributed observations. When the tails of the distribution are proportional much of extreme value statistics remains valid. The proportionality function for the tails can be estimated non-parametrically along with the (common) extreme value index. For a positive extreme value index, joint asymptotic normality of both estimators is shown; they are asymptotically independent. We also establish asymptotic…

Statistical depth measures the centrality of a point with respect to a given distribution or data cloud. It provides a natural center-outward ordering of multivariate data points and yields a systematic nonparametric multivariate analysis scheme. In particular, the half-space depth is shown to have many desirable properties and broad applicability. However, the empirical half-space depth is zero outside the convex hull of the data. This property has rendered the empirical…

Let $(X_{1},Y_{1}),\ldots,(X_{n},Y_{n})$ be an i.i.d. sample from a bivariate distribution function that lies in the max-domain of attraction of an extreme value distribution. The asymptotic joint distribution of the standardized component-wise maxima $\bigvee_{i=1}^{n}X_{i}$ and $\bigvee_{i=1}^{n}Y_{i}$ is then characterized by the marginal extreme value indices and the tail copula $R$. We propose a procedure for constructing asymptotically distribution-free goodness-of-fit…

边际期望损失的估计：当相关变量处于极端值时AI 解读

Summary Denote the loss return on the equity of a financial institution as X and that of the entire market as Y. For a given very small value of p > 0, the marginal expected shortfall (MES) is defined as E{X|Y>QY(1−p)}, where Q Y(1 − p) is the (1 − p)th quantile of the distribution of Y. The MES is an important factor when measuring the systemic risk of financial institutions. For a wide non-parametric class of bivariate distributions, we construct an estimator of the MES…

任意维度尾部依赖的 M 估计量AI 解读

Consider a random sample in the max-domain of attraction of a multivariate extreme value distribution such that the dependence structure of the attractor belongs to a parametric model. A new estimator for the unknown parameter is defined as the value that minimizes the distance between a vector of weighted integrals of the tail dependence function and their empirical counterparts. The minimization problem has, with probability tending to one, a unique, global solution. The…

多元正则变动条件下的极端风险区域估计AI 解读

When considering d possibly dependent random variables, one is often interested in extreme risk regions, with very small probability p. We consider risk regions of the form {z ∈ ℝd : f(z) ≤ β}, where f is the joint density and β a small number. Estimation of such an extreme risk region is difficult since it contains hardly any or no data. Using extreme value theory, we construct a natural estimator of an extreme risk region and prove a refined form of consistency, given a…

极值分布谱测度的最大经验似然估计AI 解读

Consider a random sample from a bivariate distribution function F in the max-domain of attraction of an extreme-value distribution function G. This G is characterized by two extreme-value indices and a spectral measure, the latter determining the tail dependence structure of F. A major issue in multivariate extreme-value theory is the estimation of the spectral measure Φp with respect to the Lp norm. For every p∈[1, ∞], a nonparametric maximum empirical likelihood estimator…

多重风险同步监测中极端事件的阈值划分AI 解读

This article develops a threshold system for monitoring airline performance. This threshold system divides the sample space into regions with increasing levels of risk and allows instant assessments of risk level of any observed airline performance. Of particular concern is the performance with extreme risk. In this article, a multivariate extreme value theory approach is used to establish thresholds for signaling varying levels of extremeness in the context of simultaneous…

利用极值理论分析田径世界纪录AI 解读

We are interested in two questions on extremes relating to world records in athletics. The first question is: What is the ultimate world record in a specific athletic event (such as the 100-m race for men or the high jump for women), given today’s state of the art? Our second question is: How “good” is a current athletic world record? An answer to the second question also enables us to compare the quality of world records in different athletic events. We consider these…

尾部 copula 过程的加权近似及二元极值条件检验AI 解读

Consider n i.i.d. random vectors on ℝ2, with unknown, common distribution function F. Under a sharpening of the extreme value condition on F, we derive a weighted approximation of the corresponding tail copula process. Then we construct a test to check whether the extreme value condition holds by comparing two estimators of the limiting extreme value distribution, one obtained from the tail copula process and the other obtained by first estimating the spectral measure which…

连续函数空间上极值估计量的渐近正态性AI 解读

Consider n i.i.d. random elements on C[0,1]. We show that, under an appropriate strengthening of the domain of attraction condition, natural estimators of the extreme-value index, which is now a continuous function, and the normalizing functions have a Gaussian process as limiting distribution. A key tool is the weak convergence of a weighted tail empirical process, which makes it possible to obtain the results uniformly on [0,1]. Detailed examples are also presented.

基于经验似然的多重分位数图置信管AI 解读

The nonparametric empirical likelihood approach is used to obtain simultaneous confidence tubes for multiple quantile plots based on $k$ independent (possibly right-censored) samples. These tubes are asymptotically distribution free, except when both $k \geq 3$ and censoring is present. Pointwise versions of the confidence tubes, however, are asymptotically distribution free in all cases. The various confidence tubes are valid under minimal conditions. The proposed methods…

广义分位数过程AI 解读

For random vectors taking values in $\mathbb{R}^d$ we introduce a notion of multivariate quantiles defined in terms of a class of sets and study an associated process which we call the generalized quantile process. This process specializes to the well known univariate quantile process. We obtain functional central limit theorems for our generalized quantile process and show that both Gaussian and non-Gaussian limiting processes can arise. A number of interesting example are…