Estimation of Multinomial Probabilities under a Model Constraint

In this paper estimation of the probabilities of a multinomial distribution has been studied. The five estimators considered are: unrestricted estimator (UE), restricted estimator (RE) (under model ), preliminary test estimator (PTE) based on a test of the model , shrinkage estimator (SE) and the positive-rule shrinkage estimator (PRSE). Asymptotic distributions of these estimators are given under Pitman alternatives and the asymptotic risk under a quadratic loss has been evaluated. The relative performance of the five estimators is then studied with respect to their asymptotic distributional risks (ADR). It is seen that neither of the preliminary test and shrinkage estimators dominates the other, though each fares well relative to the other estimators. However, the positive rule estimator is recommended for use for dimension 3 or more while the PTE is recommended for dimension less than 3.     

杭州不同功能区道路灰尘中污染物的分布和有效性

比较研究了杭州城市的工业区、商业区、居民区、公园和附近农村道路灰尘中重金属(Pb、Cu、Cd、Zn、Hg)、P和有机物的积累情况,测定了灰尘分散到水中后污染物在溶液、悬浮物和沉积物中的分配情况。结果表明,不同功能区城市灰尘中污染物含量有较大的变异:重金属一般以工业区和商业区为最高;P以居民区和商业区为最高,而有机物以公园和居民区最高;灰尘中污染物含量随粒径减小而增加。当灰尘分散至水中后,重金属等污染物大部分以沉积相形式存在,少量以溶解相和悬浮相存在;溶解态重金属的比例均较低,平均在0.5%以下,其中ρ(Hg)、ρ(Cd)>ρ(Zn)、ρ(Cu)>ρ(Pb)。而生物有效态(双酸提取)重金属占其总量的比例平均在12%~29%之间,由高到低顺序为Zn,Cd,Cu,Hg,Pb。     

含一般模糊弹性约束的广义模糊变量线性规划

建立并讨论了一类含有一般模糊弹性约束的广义模糊变量线性规划问题.首先,简单介绍了结构元方法并对结构元加权排序中权函数表征决策者风险态度进行了深入分析.然后选取风险中性的决策者来定义序关系,应用Verdegay模糊线性规划方法将含一般模糊弹性约束的广义模糊变量线性规划转化经典的线性规划问题,简化了原问题的求解.最后通过数值算例进一步说明了该方法的有效性.     

The Occurrence of Pesticides in Groundwater—Results of Case-studies

Abstract

A comparative review of pesticide survey endosing 16 waterworks in the FRG tries to increase the understanding about interferences of pesticide utilization and pesticide occurrence in ground- and drinkingwater, which includes characterization of sampling points, subsurface situation, land use and pesticide application. Between 1986 and 1991, 5772 samples were measured and led to 219094 data about the occurrence of various pesticides. 5% of these analyses showed pesticide or metabolite concentrations above the particular detection limits. This result does not vary in large extent considering groups of different characterized sampling points like groundwater dominated or surface water sampling points. As the herbicide atrazine and its metabolite desethylatrazine as well as the herbicide simazine were detected most often in all samples independent whether considering groundwater und surface water samples, this fact confirms the FRG-application ban for atrazine as well as the application restriction for simazine.     

基于灰色聚类分析的风险评价方法研究——以江苏民间资本进入金融领域风险评价为例

运用灰色系统理论,结合AHP方法,建立灰色聚类分析模型,对风险进行评价,并以江苏民间资本进入金融领域风险评价为例进行研究.结果表明,民间资本进入金融领域的风险属于高风险范畴,其中进入风险中的产业风险和社会风险属于高风险,信用风险属于较高风险,政治风险属于中等风险.并针对上述风险的等级,提出了相应的政策建议.模型具有一定的实用价值,它对于正确认识民间资本进入金融领域的风险和有针对性地制定相应的政策措施具有一定的理论和现实意义.     

Dynamic models of segregation†

Some segregation results from the practices of organizations, some from specialized communication systems, some from correlation with a variable that is non‐random; and some results from the interplay of individual choices. This is an abstract study of the interactive dynamics of discriminatory individual choices. One model is a simulation in which individual members of two recognizable groups distribute themselves in neighborhoods defined by reference to their own locations. A second model is analytic and deals with compartmented space. A final section applies the analytics to ‘neighborhood tipping.’ The systemic effects are found to be overwhelming: there is no simple correspondence of individual incentive to collective results. Exaggerated separation and patterning result from the dynamics of movement. Inferences about individual motives can usually not be drawn from aggregate patterns. Some unexpected phenomena, like density and vacancy, are generated. A general theory of ‘tipping’ begins to emerge.     

Intensity‐based estimation of extreme loss event probability and value at risk

We develop a methodology for the estimation of extreme loss event probability and the value at risk, which takes into account both the magnitudes and the intensity of the extreme losses. Specifically, the extreme loss magnitudes are modeled with a generalized Pareto distribution, whereas their intensity is captured by an autoregressive conditional duration model, a type of self‐exciting point process. This allows for an explicit interaction between the magnitude of the past losses and the intensity of future extreme losses. The intensity is further used in the estimation of extreme loss event probability. The method is illustrated and backtested on 10 assets and compared with the established and baseline methods. The results show that our method outperforms the baseline methods, competes with an established method, and provides additional insight and interpretation into the prediction of extreme loss event probability. Copyright © 2012 John Wiley & Sons, Ltd.     

Weber Correspondence Analysis: The One-Dimensional Case

When designing programs or software for the implementation of Monte Carlo (MC) hypothesis tests, we can save computation time by using sequential stopping boundaries. Such boundaries imply stopping resampling after relatively few replications if the early replications indicate a very large or a very small p value. We study a truncated sequential probability ratio test (SPRT) boundary and provide a tractable algorithm to implement it. We review two properties desired of any MC p value, the validity of the p value and a small resampling risk, where resampling risk is the probability that the accept/reject decision will be different than the decision from complete enumeration. We show how the algorithm can be used to calculate a valid p value and confidence intervals for any truncated SPRT boundary. We show that a class of SPRT boundaries is minimax with respect to resampling risk and recommend a truncated version of boundaries in that class by comparing their resampling risk (RR) to the RR of fixed boundaries with the same maximum resample size. We study the lack of validity of some simple estimators of p values and offer a new, simple valid p value for the recommended truncated SPRT boundary. We explore the use of these methods in a practical example and provide the MChtest R package to perform the methods.     

Hedging mortality/longevity risks of insurance portfolios for life insurer/annuity provider and financial intermediary

In this paper, we propose two risk hedge schemes in which a life insurer (an annuity provider) can transfer mortality (longevity) risk of a portfolio of life (annuity) exposures to a financial intermediary by paying the hedging premium of a mortality-linked security. The optimal units of the mortality-linked security which maximize hedge effectiveness for a life insurer (an annuity provider) can be derived as closed-form formulas under the risk hedge schemes. Numerical illustrations show that the risk hedge schemes can significantly hedge the downside risk of loss due to mortality (longevity) risk for the life insurer (annuity provider) under some stochastic mortality models. Besides, finding an optimal weight of a portfolio of life and annuity business, the financial intermediary can reduce the sensitivity to mortality rates but the model risk; a security loading may be imposed on the hedge premium for a higher probability of gain to compensate the financial intermediary for the inevitable model risk.     

Asymptotic estimates of Gerber-Shiu functions in the renewal risk model with exponential claims

This paper continues to study the asymptotic behavior of Gerber-Shiu expected discounted penalty functions in the renewal risk model as the initial capital becomes large. Under the assumption that the claim-size distribution is exponential, we establish an explicit asymptotic formula. Some straightforward consequences of this formula match existing results in the field.