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两步分位数回归中 CoVaR 推断的渐近理论AI 解读

Measuring systemic risk has been an important topic in recent research on risk management. Adrian and Brunnermeier (2016) pioneered the CoVaR measure for systemic risk, which is defined as the conditional quantile of system loss given some state predictors and one stress event of an individual loss at a certain risk level. They proposed to estimate CoVaR by a two-quantile-regression approach, which is simple and easy to implement in practice, but without stating or…

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…

稠密因子增强模型下的岭回归AI 解读

This article establishes a comprehensive theory of the optimality, robustness, and cross-validation selection consistency for the ridge regression under factor-augmented models with possibly dense idiosyncratic information.Using spectral analysis for random matrices, we show that the ridge regression is asymptotically efficient in capturing both factor and idiosyncratic information by minimizing the limiting predictive loss among the entire class of spectral regularized…

异质幂律数据的极值推断AI 解读

We extend extreme value statistics to independent data with possibly very different distributions. In particular, we present novel asymptotic normality results for the Hill estimator, which now estimates the extreme value index of the average distribution. Due to the heterogeneity, the asymptotic variance can be substantially smaller than that in the i.i.d. case. As a special case, we consider a heterogeneous scales model where the asymptotic variance can be calculated…

针对高维局部备择序列的最强检验AI 解读

We develop a powerful quadratic test for the overall significance of many covariates in a dense regression model in the presence of nuisance parameters. By equally weighting the sample moments, the test is asymptotically correct in high dimensions even when the number of coefficients is larger than the sample size. Our theory allows a non-parametric error distribution and weakly exogenous nuisance variables, in particular autoregressors in many applications. Using random…

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…

基于广义帕累托分布的风险分析AI 解读

We compute the value-at-risk of financial losses by fitting a generalized Pareto distribution to exceedances over a threshold. Following the common practice of setting the threshold as high sample quantiles, we show that, for both independent observations and time-series data, the asymptotic variance for the maximum likelihood estimation depends on the choice of threshold, unlike the existing study of using a divergent threshold. We also propose a random weighted bootstrap…

预测回归中条件风险价值的统计推断AI 解读

Conditional value-at-risk is a popular risk measure in risk management. We study the inference problem of conditional value-at-risk under a linear predictive regression model. We derive the asymptotic distribution of the least squares estimator for the conditional value-at-risk. Our results relax the model assumptions made in (Oper. Res. 60 (2012) 739–756) and correct their mistake in the asymptotic variance expression. We show that the asymptotic variance depends on the…

相对风险度量的统计推断AI 解读

For monitoring systemic risk from regulators’ point of view, this article proposes a relative risk measure, which is sensitive to the market comovement. The asymptotic normality of a nonparametric estimator and its smoothed version is established when the observations are independent. To effectively construct an interval without complicated asymptotic variance estimation, a jackknife empirical likelihood inference procedure based on the smoothed nonparametric estimation is…

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…