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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…

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…

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…