基于病例队列数据的比例风险模型的诊断

病例队列设计是一种在生存分析中广泛应用的可以降低成本又能提高效率的抽样方法.对于病例队列数据,已经有很多统计方法基于比例风险模型来估计协变量对生存时间的影响.然而,很少有工作基于病例队列数据来检验模型的假设是否成立.在这篇文章中,我们基于渐近的零均的值随机过程提出了一类检验统计量,这类检验统计量可以基于病例队列数据来检验比例风险模型的假设是否成立.我们通过重抽样的方法来逼近上述检验统计量的渐近分布,通过数值模拟来研究所提方法在有限样本下的表现,最后将所提出的方法应用于一个国家肾母细胞瘤研究的真实数据集上.     

基于分段损失分布法和Copula的银行操作风险集成度量

多个风险单元的集成度量是银行操作风险管理的关键步骤之一。立足于操作风险的“厚尾”、“截断”性,从分段损失分布法的视角出发,探讨操作风险集成度量的模式和数值方法。首先,引入两阶段损失分布法来拟合单个风险单元边际损失分布,用双截尾分布代替传统的完整分布来刻画“高频低损”损失数据的双截断特性,利用POT模型捕获“低频高损”事件的厚尾特性。再次,基于分段建模思路,对传统度量过程中边际分布为单一、完整分布的Copula模型进行了扩展,研究边际分布为分段分布、截尾分布条件下使用Copula函数集成度量操作风险的框架和步骤,并设计了Monte Carlo模拟算法。最后,以实证分析的形式验证所构建模型。通过对中国商业银行416个操作风险损失数据的实证分析,结果表明分段分布、截尾分布能对单个风险单元边际分布有更好的拟合效果,能减小由于分布选择不当而引发的模型风险。分段度量视角下Copula函数的引入能灵活处理多个操作风险单元间的相依结构,使风险度量结果更为合理。     

Logistic回归模型的影响分析

Logistic回归模型的影响分析是Logistic回归诊断研究中的重要内容。常用的分析方法都是轮换地删除数据点后的逐步判断,而这个判断的过程主要体现在模型的诊断图上。鉴于此,通过构造诊断统计量来有效地开发诊断图成为影响分析的核心内容,并由此能较为准确地探寻出模型的强影响点。本文通过对Logistic回归模型帽子矩阵的分解以及对轮换地删除数据点后的系数估计的相对变化量进行加权,得出Logistic回归模型诊断图使其能比传统的诊断图更准确地判断出模型的强影响点。     

基于熵权修正Shapley值法的共同物流商业模式合作风险分担研究

共同物流参与主体间的风险分担机制是共同物流商业模式稳健运行的一个关键问题.共同物流主体间的合作风险包括道德风险、管理风险、运作风险以及信用风险,在四类风险结构分析的基础上,构建共同物流商业模式合作风险评价指标体系,采用截尾平均数表示专家评估风险损失值的Shapley值法,以利用熵权法进行Shapley值修正,构建共同物流商业模式合作风险分担模型,通过实例分析验证模型,给出共同物流商业模式合作风险分担机制的优化路径.     

个人信用评分的Adaptive Lasso-Logistic回归分析

以个人信用风险为研究对象,分析影响个人信用评分的因素.利用某商业银行个人信用数据,并采用.Adaptive Lasso-Logistic回归模型对影响顾客的个人信用风险的因素进行分析,并与传统Logistic回归模型以及Lasso-Logistic回归模型进行比较.以对顾客"好"与"坏"的二分类结果的正确比例为主要衡量标准,实证发现以.Adaptive Lassi-Logistic回归方法建立的个人信用评分模型,在变量选择和解释上,以及预测的准确性上,均优于传统的Logistic和Lasso-Logistic方法.     

比例风险模型下参数估计的两种MM算法的一些应用

对于带有删失机制的生存数据的研究,比例风险模型是应用最为广泛的统计模型之一。实际中,为得到其参数的极大似然估计需要采用数值方法计算得分方程的解。MinorizationMaximization算法(以下简称"MM算法")将求解复杂的目标函数的极值问题转化为求解简单的代理函数的极值问题。本文主要探讨,在比例风险模型下通过两种不同的思想为偏似然函数构造代理函数,从而得到的两种MM算法。通过数值模拟和实际数据分析实现这两种MM算法在比例风险模型下的一些应用。     

高血压性脑出血再发生因素的Logistic分析

根据问题的特点，选择Logistic判别模型，并借鉴普通线性回归的逐步向前法，用似然比统计量（Deviance）来筛选自变量（因素）。结果显示：在11个因素中，有3个是作用显著的，而其中舒张压值极为重要。为降低再出血率，将其控制在85mmHg以下是有效而可行的。     

多总体死亡率差异风险度量——以ILS债券为例

在回顾多总体动态死亡率预测模型研究成果的基础上,简要评述了已有模型的适应情况和假设条件,并依此构建了死亡率差异风险的度量模型.此后,并以ILS债券为例,利用HMD数据库中英国和美国人口死亡率数据,使用构建的死亡率差异风险度量模型,测量了ILS债券中的死亡率差异风险.定量分析结果显示:ILS为投资者设定了较高的安全阀值,保障了ILS的成功发行.     

基于贝叶斯极值估计的商业银行内部欺诈风险度量研究

内部欺诈风险是我国商业银行面临的一个重大风险来源。本文针对内部欺诈具有的低频率高损失的特点,采用不同分布分段刻画其损失统计分布规律,对于低于和高于门限值的样本点,采用Box-Cox变换和全Paretian分布模型进行分析,然后采用贝叶斯估计对全Paretian分布模型的参数进行估计,接着在此基础上对建立了一个内部欺诈风险度量模型,然后使用所构建的风险度量模型对操作风险在险风险值、经济资本和最大可能损失进行了测算,最后提出了防范操作风险的政策建议。     

代谢综合征风险、趋势预测和干预模型的构建

结合基因组学数据与生物学背景,利用数学与统计的方法研究代谢综合征的致病机理。首先,利用变异系数筛选出信息含量较高的数据,并且利用变异基因频数统计的方法确定高频变异基因。通过查阅相关文献和数据库可知,大部分高频变异基因都与代谢综合征有关。随后,研究高频变异基因对其他基因的调控情况,并且由此构建出高频变异基因的调控网络以及网络内部的协同和拮抗作用。最后,提出基于调控网络的患病风险预测模型,由此提供预防或治疗方案。     

企业诚信度的贝叶斯估计研究

本文利用贝叶斯分析方法建立了评估企业诚信度的概率估计模型，并选取了一些有代表性的企业进行实证分析。与现有的同类问题研究相比，本模型的特点是将决策者个人经验和主观判断作为先验信息与样本信息相结合、将财务数据与诚信表现相结合，从而提高了估计的可靠性和准确性。     

部分线性模型中的非参数部分的线性性检验

In this paper,we propose the test statistic to check whether the nonpara- metric function in partially linear models is linear or not.We estimate the nonpara- metric function in alternative by using the local linear method,and then estimate the parameters by the two stage method.The test statistic under the null hypothesis is calculated,and it is shown to be asymptotically normal.     

A semiparametric Wald statistic for testing logistic regression models based on case-control data

We propose a semiparametric Wald statistic to test the validity of logistic regression models based on case-control data. The test statistic is constructed using a semiparametric ROC curve estimator and a nonparametric ROC curve estimator. The statistic has an asymptotic chisquared distribution and is an alternative to the Kolmogorov-Smirnov-type statistic proposed by Qin and Zhang in 1997, the chi-squared-type statistic proposed by Zhang in 1999 and the information matrix test statistic proposed by Zhang in 2001. The statistic is easy to compute in the sense that it requires none of the following methods: using a bootstrap method to find its critical values, partitioning the sample data or inverting a high-dimensional matrix. We present some results on simulation and on analysis of two real examples. Moreover, we discuss how to extend our statistic to a family of statistics and how to construct its Kolmogorov-Smirnov counterpart. This work was supported by the 11.5 Natural Scientific Plan (Grant No. 2006BAD09A04) and Nanjing University Start Fund (Grant No. 020822410110)     

Improved estimates for multivariate complex-normal regression with application to analysis of linear time-invariant relationships

The objective of this paper is the estimation of linear time-invariant relationships for a stationary vector-valued time series using the Finite Fourier Transform as the basic statistic. Since this is asymptotically complex-Normal we are led to consider models of multivariate complex-Normal regression. We propose estimates of regression matrices in the tradition of Stein (shrunken estimates) which improve upon the usual estimates. Some experience with simulated time series is reported.     

Transmission of macroeconomic shocks to risk parameters: Their uses in stress testing

In this paper, we are interested in evaluating the resilience of financial portfolios under extreme economic conditions. Therefore, we use empirical measures to characterize the transmission process of macroeconomic shocks to risk parameters. We propose the use of an extensive family of models, called General Transfer Function Models, which condense well the characteristics of the transmission described by the impact measures. The procedure for estimating the parameters of these models is described employing the Bayesian approach and using the prior information provided by the impact measures. In addition, we illustrate the use of the estimated models from the credit risk data of a portfolio.     

Inference of change-point in single index models

Single index models are widely used in medicine, econometrics and some other fields. In this paper, we consider the inference of a change point problem in single index models. Based on density-weighted average derivative estimation (ADE) method, we propose a statistic to test whether a change point exists or not. The null distribution of the test statistic is obtained using a permutation technique. The permuted statistic is rigorously shown to have the same distribution in the limiting sense under both null and alternative hypotheses. After the null hypothesis of no change point is rejected, an ADE-based estimate of the change point is proposed under assumption that the change point is unique. A simulation study confirms the theoretical results.     

Classification analysis for simulation of the duration of machine breakdowns

Machine failure can have a significant impact on the throughput of manufacturing systems, therefore accurate modelling of breakdowns in manufacturing simulation models is essential. Finite mixture distributions have been successfully used by Ford Motor Company to model machine breakdown durations in simulation models of engine assembly lines. These models can be very complex, with a large number of machines. To simplify the modelling we propose a method of grouping machines with similar distributions of breakdown durations, which we call the Arrows Classification Method, where the Two-Sample Cramér-von-Mises statistic is used to measure the similarity of two sets of the data. We evaluate the classification procedure by comparing the throughput of a simulation model when run with mixture models fitted to individual machine breakdown durations; mixture models fitted to group breakdown durations; and raw data. Details of the methods and results of the classification will be presented, and demonstrated using an example.     

基于改进加权Poisson CUSUM控制图的发病率监控研究

现代社会医疗质量管理的重要性不言而喻,如何科学有效地开展发病率监控,具有重要的研究意义和实用价值。本文主要研究加权Poisson CUSUM控制图的改进及其在发病率监控上的应用。通过引入"标准化"处理思想,即将对数似然比统计量除以对应样本容量,本文提出"标准化"对数似然比加权Poisson CUSUM控制图,用以提高对发病率的监控水平。通过设定合适的人口模型,模拟计算验证了本文设计的模型能够有效提高监控效果,且对于不同人口模型和不同加权函数均有显著优势。最后,基于美国新墨西哥州男性甲状腺癌患病数据开展的实证检验也印证了以上结论。     

Multi-population mortality models: A factor copula approach

Modeling mortality co-movements for multiple populations have significant implications for mortality/longevity risk management. A few two-population mortality models have been proposed to date. They are typically based on the assumption that the forecasted mortality experiences of two or more related populations converge in the long run. This assumption might be justified by the long-term mortality co-integration and thus be applicable to longevity risk modeling. However, it seems too strong to model the short-term mortality dependence. In this paper, we propose a two-stage procedure based on the time series analysis and a factor copula approach to model mortality dependence for multiple populations. In the first stage, we filter the mortality dynamics of each population using an ARMA–GARCH process with heavy-tailed innovations. In the second stage, we model the residual risk using a one-factor copula model that is widely applicable to high dimension data and very flexible in terms of model specification. We then illustrate how to use our mortality model and the maximum entropy approach for mortality risk pricing and hedging. Our model generates par spreads that are very close to the actual spreads of the Vita III mortality bond. We also propose a longevity trend bond and demonstrate how to use this bond to hedge residual longevity risk of an insurer with both annuity and life books of business.     

Efficient option risk measurement with reduced model risk

Options require risk measurement that is also computationally efficient as it is important to derivatives risk management. There are currently few methods that are specifically adapted for efficient option risk measurement. Moreover, current methods rely on series approximations and incur significant model risks, which inhibit their applicability for risk management.In this paper we propose a new approach to computationally efficient option risk measurement, using the idea of a replicating portfolio and coherent risk measurement. We find our approach to option risk measurement provides fast computation by practically eliminating nonlinear computational operations. We reduce model risk by eliminating calibration and implementation risks by using mostly observable data, we remove internal model risk for complex option portfolios by not admitting arbitrage opportunities, we are also able to incorporate liquidity or model misspecification risks. Additionally, our method enables tractable and convex optimisation of portfolios containing multiple options. We conduct numerical experiments to test our new approach and they validate it over a range of option pricing parameters.