考虑风险关联情形的风险评估方法研究

针对多个风险之间存在关联的风险评估问题,给出了一种风险评估方法。在本文中,首先依据专家小组给出关于风险关联的评价信息,通过构建综合关联矩阵识别风险之间的影响关系,进而确定风险的层次结构;然后依据确定的可划分或不可划分的风险层次结构以及专家小组给出的风险发生的概率和风险损失,运用概率论相关知识来计算各风险值。最后,通过一个算例说明了本文提出方法的可行性和有效性。  

Improved estimation under collinearity and squared error loss

This paper examines the performance of several biased, Stein-like and empirical Bayes estimators for the general linear statistical model under conditions of collinearity. A new criterion for deleting principal components, based on an unbiased estimator of risk, is introduced. Using a squared error measure and Monte Carlo sampling experiments, the resulting estimator's performance is evaluated and compared with other traditional and non-traditional estimators.  

Improved estimators for the GMANOVA problem with application to Monte Carlo simulation

The problem of finding classes of estimators which improve upon the usual (e.g., ML, LS) estimator of the parameter matrix in the GMANOVA model under (matrix) quadratic loss is considered. Classes of improved estimators are obtained via combining integration-by-parts methods for normal and Wishart distributions. Also considered is the application of control variates to achieve better efficiency in multipopulation multivariate simulation studies.  

Bootstrap choice of tuning parameters

Consider the problem of estimating θ=θ(P) based on datax _n from an unknown distributionP. Given a family of estimatorsT _{n, β} of θ(P), the goal is to choose β among β∈I so that the resulting estimator is as good as possible. Typically, β can be regarded as a tuning or smoothing parameter, and proper choice of β is essential for good performance ofT _{n, β} . In this paper, we discuss the theory of β being chosen by the bootstrap. Specifically, the bootstrap estimate of β, , is chosen to minimize an empirical bootstrap estimate of risk. A general theory is presented to establish the consistency and weak convergence properties of these estimators. Confidence intervals for θ(P) based on , are also asymptotically valid. Several applications of the theory are presented, including optimal choice of trimming proportion, bandwidth selection in density estimation and optimal combinations of estimates.  

The opportunity cost of mean–variance choice under estimation risk

Mean–variance portfolio choice is often criticized as sub-optimal in the more general expected utility framework. It is argued that the expected utility framework takes into consideration higher moments ignored by mean variance analysis. A body of research suggests that mean–variance choice, though arguably sub-optimal, provides very close-to-expected utility maximizing portfolios and their expected utilities, basing its evaluation on in-sample analysis where mean–variance choice is sub-optimal by definition. In order to clarify this existing research, this study provides a framework that allows comparing in-sample and out-of-sample performance of the mean variance portfolios against expected utility maximizing portfolios. Our in-sample results confirm the results of earlier studies. On the other hand, our out-of-sample results show that the expected utility model performs worse. The out-of-sample inferiority of the expected utility model is more pronounced for preferences and constraints under which in-sample mean variance approximations are weakest. We argue that, in addition to its elegance and simplicity, the mean–variance model extracts more information from sample data because it uses the covariance matrix of returns. The expected utility model may reach its optimal solution without using information from the covariance matrix.  

基于蒙特卡罗模拟的供应链风险估计研究

以市场需求波动风险为例,基于蒙特卡罗模拟研究了供应链风险估计问题.首先,对市场需求波动风险及其损失度量进行理论分析,利用市场需求波动风险情境下的供应链系统库存成本损失来度量市场需求波动风险的损失.其次,选择供应链末端需求为蒙特卡罗方法待模拟的随机变量,基于需求建立了市场需求波动风险概率测度模型和风险损失度量模型,确定了市场需求波动风险概率和风险损失为需求的相关量.然后,通过实例的仿真求解验证了模型.最后,给出了利用本模型方法进行供应链风险估计时需要注意的问题及进一步研究的问题.研究表明:蒙特卡罗方法对供应链风险估计具有较强的鲁棒性.  

Shrinkage estimators for large covariance matrices in multivariate real and complex normal distributions under an invariant quadratic loss

The problem of estimating large covariance matrices of multivariate real normal and complex normal distributions is considered when the dimension of the variables is larger than the number of samples. The Stein–Haff identities and calculus on eigenstructure for singular Wishart matrices are developed for real and complex cases, respectively. By using these techniques, the unbiased risk estimates for certain classes of estimators for the population covariance matrices under invariant quadratic loss functions are obtained for real and complex cases, respectively. Based on the unbiased risk estimates, shrinkage estimators which are counterparts of the estimators due to Haff [L.R. Haff, Empirical Bayes estimation of the multivariate normal covariance matrix, Ann. Statist. 8 (1980) 586–697] are shown to improve upon the best scalar multiple of the empirical covariance matrix under the invariant quadratic loss functions for both real and complex multivariate normal distributions in the situation where the dimension of the variables is larger than the number of samples.  

Approximate Bayes estimators applied to the Bilal model

This paper develops approximate Bayes estimators of the parameter of the Bilal failure model by using the method of Tierney and Kadane [Accurate approximations for posterior moments and marginal densities, J. Amer. Statist. Assoc. 81 (1986) 82–86.] based on Type-2 censored sample and four different loss functions. Existence and uniqueness theorem for the maximum likelihood estimate are established. Based on Monte Carlo simulation study, comparisons are made between those estimators and their corresponding Bayes estimators obtained by using Gibb’s sampling approach.  

Multiple Penalty Regression: Fitting and Extrapolating a Discrete Incomplete Multi-way Layout

The d iscrete multi-way layout is an abstract data type associated with regression, experimental designs, digital images or videos, spatial statistics, gene or protein chips, and more. The factors influencing response can be nominal or ordinal. The observed factor level combinations are finitely discrete and often incomplete or irregularly spaced. This paper develops low risk biased estimators of the means at the observed factor level combinations; and extrapolates the estimated means to larger discrete complete layouts. Candidate penalized least squares (PLS) estimators with multiple quadratic penalties express competing conjectures about each of the main effects and interactions in the analysis of variance decomposition of the means. The candidate PLS estimator with smallest estimated quadratic risk attains, asymptotically, the smallest risk over all candidate PLS estimators. In the theoretical analysis, the dimension of the regression space tends to infinity. No assumptions are made about the unknown means or about replication.  

ASP fits to multi-way layouts

The balanced complete multi-way layout with ordinal or nominal factors is a fundamental data-type that arises in medical imaging, agricultural field trials, DNA microassays, and other settings where analysis of variance (ANOVA) is an established tool. ASP algorithms weigh competing biased fits in order to reduce risk through variance-bias tradeoff. The acronym ASP stands for Adaptive Shrinkage of Penalty bases. Motivating ASP is a penalized least squares criterion that associates a separate quadratic penalty term with each main effect and each interaction in the general ANOVA decomposition of means. The penalty terms express plausible conjecture about the mean function, respecting the difference between ordinal and nominal factors. Multiparametric asymptotics under a probability model and experiments on data elucidate how ASP dominates least squares, sometimes very substantially. ASP estimators for nominal factors recover Stein's superior shrinkage estimators for one- and two-way layouts. ASP estimators for ordinal factors bring out the merits of smoothed fits to multi-way layouts, a topic broached algorithmically in work by Tukey. This research was supported in part by National Science Foundation Grants DMS 0300806 and 0404547.