基于LGCNET多层网络的中国A股上市公司系统性风险度量

系统性风险度量一直是金融风险领域的热点问题,但是对于复杂网络条件下的度量方法还缺乏深入研究。本文将滑动窗口分位数回归与局部高斯相关方法相结合,构建出一种全新的多层时变网络——局部高斯相关网络(Local Gaussian Correlation Network, LGCNET)。基于此方法,本文通过研究中国证券市场股票总体及尾部收益的非线性相关性,分析了2018年至2021年我国A股50家上市企业关联网络的演化特征,通过考察金融网络系统性风险水平在整个时间段内的变化情况,探究了新冠疫情及中美贸易摩擦期间上市公司网络的风险变化情况。结果表明：第一,金融与科技行业是网络节点的中心,与其他行业公司存在较高关联性,表明该类行业是风险传导的中心。第二,基建及银行类公司因为其市值高,在系统中的重要程度普遍较高;同时,尾部风险排名高于其市值排名的企业具有较大市场影响力和风险传导能力,也应该受到关注。第三,在系统层面,受信用风险加剧及中美贸易摩擦的影响,2018年整个网络系统普遍具有较高风险水平;但在2020年新冠疫情期间,国内系统性风险一直控制在较低水平。     

左模张量积的同态及其基础环的转移

本文在[1]的基础上，讨论了两个左模张量积的同态，左模和左模张量积的基础环的转移，逆转移。并给出了基础环逆转移的一个同构定理。     

分块Z-循环矩阵的逆与Moore-Penrose逆的一个算法

本文给出了分块Z-循环矩阵的逆与Moorc-Pcnrosc逆的一个算法。     

Bayesian inference for non-stationary spatial covariance structure via spatial deformations

Summary. In geostatistics it is common practice to assume that the underlying spatial process is stationary and isotropic, i.e. the spatial distribution is unchanged when the origin of the index set is translated and under rotation about the origin. However, in environmental problems, such assumptions are not realistic since local influences in the correlation structure of the spatial process may be found in the data. The paper proposes a Bayesian model to address the anisot- ropy problem. Following Sampson and Guttorp, we define the correlation function of the spatial process by reference to a latent space, denoted by D , where stationarity and isotropy hold. The space where the gauged monitoring sites lie is denoted by G . We adopt a Bayesian approach in which the mapping between G and D is represented by an unknown function d (·). A Gaussian process prior distribution is defined for d (·). Unlike the Sampson–Guttorp approach, the mapping of both gauged and ungauged sites is handled in a single framework, and predictive inferences take explicit account of uncertainty in the mapping. Markov chain Monte Carlo methods are used to obtain samples from the posterior distributions. Two examples are discussed: a simulated data set and the solar radiation data set that also was analysed by Sampson and Guttorp.     

Adjusting overall survival for treatment switches: commonly used methods and practical application

In parallel group trials, long‐term efficacy endpoints may be affected if some patients switch or cross over to the alternative treatment arm prior to the event. In oncology trials, switch to the experimental treatment can occur in the control arm following disease progression and potentially impact overall survival. It may be a clinically relevant question to estimate the efficacy that would have been observed if no patients had switched, for example, to estimate ‘real‐life’ clinical effectiveness for a health technology assessment. Several commonly used statistical methods are available that try to adjust time‐to‐event data to account for treatment switching, ranging from naive exclusion and censoring approaches to more complex inverse probability of censoring weighting and rank‐preserving structural failure time models. These are described, along with their key assumptions, strengths, and limitations. Best practice guidance is provided for both trial design and analysis when switching is anticipated. Available statistical software is summarized, and examples are provided of the application of these methods in health technology assessments of oncology trials. Key considerations include having a clearly articulated rationale and research question and a well‐designed trial with sufficient good quality data collection to enable robust statistical analysis. No analysis method is universally suitable in all situations, and each makes strong untestable assumptions. There is a need for further research into new or improved techniques. This information should aid statisticians and their colleagues to improve the design and analysis of clinical trials where treatment switch is anticipated. Copyright © 2013 John Wiley & Sons, Ltd.     

On asymptotics of multivariate integrals with applications to records

Let { X _n ,n≥1} be a sequence of iid. Gaussian random vectors in R ^d , d≥2, with nonsingular distribution function F. In this paper the asymptotics for the sequence of integrals I _F,n (G _n )?n∫ _{R ^d} G _n ^n?1( X ) dF( X ) is considered with G _n some distribution function on R ^d . In the case G _n =F the integral I _F,n (F)/n is the probability that a record occurs in X ₁,…, X _n at index n. [1] Gnedin, A.V. 1998. Records from a Multivariate Normal Sample. Statist. Probab. Lett., 39: 11–15. [Crossref], [Web of Science ®] , [Google Scholar] obtained lower and upper asymptotic bounds for this case, whereas [2] Ledford, W.A. and Twan, A.J. 1998. On the Tail Concomitant Behaviour for Extremes. Adv. Appl. Probab., 30: 197–215. [Crossref], [Web of Science ®] , [Google Scholar] showed the rate of convergence if d=2. In this paper we derive the exact rate of convergence of I _F,n (G _n ) for d≥2 under some restrictions on the distribution function G _n . Some related results for multivariate Gaussian tails are discussed also.     

The Self‐Similar and Multifractal Nature of a Network Traffic Model

Abstract

We look at a family of models for Internet traffic with increasing input rates and consider approximation models which exhibit self‐similarity at large time scales and multifractality at small time scales. Depending on whether the input rate is fast or slow, the total cumulative input traffic can be approximated by a self‐similar stable Lévy motion or a self‐similar Gaussian process. The stable Lévy limit does not depend on the behavior of the individual transmission schedules but the Gaussian limit does. Also, the models and their approximations show multifractal behavior at small time scales.     

On the matrix-variate generalized hyperbolic distribution and its Bayesian applications

In the first part of the paper, we introduce the matrix-variate generalized hyperbolic distribution by mixing the matrix normal distribution with the matrix generalized inverse Gaussian density. The p-dimensional generalized hyperbolic distribution of [Barndorff-Nielsen, O. (1978). Hyperbolic distributions and distributions on hyperbolae. Scand. J. Stat., 5, 151–157], the matrix-T distribution and many well-known distributions are shown to be special cases of the new distribution. Some properties of the distribution are also studied. The second part of the paper deals with the application of the distribution in the Bayesian analysis of the normal multivariate linear model.     

The independent factor analysis approach to latent variable modelling

Independent factor analysis (IFA) has recently been proposed in the signal processing literature as a way to model a set of observed variables through linear combinations of latent independent variables and a noise term. A peculiarity of the method is that it defines a probability density function for the latent variables by mixtures of Gaussians. The aim of this paper is to cast the method into a more rigorous statistical framework and to propose some developments. In the first part, we present the IFA model in its population version, address identifiability issues and draw some parallels between the IFA model and the ordinary factor analysis (FA) one. Then we show that the IFA model may be reinterpreted as an independent component analysis-based rotation of an ordinary FA solution. We also give evidence that the IFA model represents a special case of mixture of factor analysers. In the second part, we address inferential issues, also deriving the standard errors for the model parameter estimates and providing model selection criteria. Finally, we present some empirical results on real data sets.     

Correcting the bias due to dependent censoring of the survival estimator by conditioning

We consider the conditional estimation of the survival function of the time T₂ to a second event as a function of the time T₁ to a first event when there is a censoring mechanism acting on their sum T₁+T₂. The problem has been motivated by a treatment interruption study aimed at improving the quality of life of HIV-infected patients. We base the analysis on the survival function of T₂ given that T₁∈I, where I represents a period of scientific interest (1 trimester, 1 year, 2 years, etc.) and propose a non-parametric estimator for the survival function of T₂ given that T₁∈I, which takes into account both the selection bias and the heterogeneity due to the dependent censoring. The proposed estimator for the survival function uses the risk group of T₂ conditioned on the categories of T₁ and corrects for the dependent censoring using weights defined by the observed values of T₁. The estimator, properly normalized, converges weakly to a zero-mean Gaussian process. We estimate the variance of the limiting process via a bootstrap methodology. Properties of the proposed estimator are illustrated by an extensive simulation study. The motivating data set is analysed by means of this new methodology.