Bayesian Risk Ratio Analysis

The classical confidence interval approach has failed to find exact intervals, or even a consensus on the best approximate intervals, for the ratio of two binomial probabilities, the so-called risk ratio. The problem is reexamined from a Bayesian viewpoint, and a simple graphical presentation of the risk ratio assessment is given in such a way that sensitivity to the selected prior distribution can be readily examined.     

On the almost sure convergence for sums of negatively superadditive dependent random vectors in Hilbert spaces and its application

Abstract

This paper develops almost sure convergence for sums of negatively superadditive dependent random vectors in Hilbert spaces, we obtain Chung type SLLN and the Jaite type SLLN for sequences of negatively superadditive dependent random vectors in Hilbert spaces. Rate of convergence is studied through considering almost sure convergence to 0 of tail series. As an application, the almost sure convergence of degenerate von Mises-statistics is investigated.     

不均等选择概率下的加权调整研究

从不均等选择概率的角度,提出两类常见的权数调整类型及其调整方法:一是规模调整,使得样本单元权数之和等于总体规模;二是结构调整,使得样本结构和总体结构一致,并构造出加权调整的设计效应模型,应用于复杂样本设计。案例分析显示,加权调整往往导致设计效应变大,带来负的效应,但校准调整能降低设计效应,提高估计精度。     

V aR 之下厚尾分布的最优资产组合的收敛性

主要研究在V aR 风险度量之下, 收益具有厚尾性质的资产的投资组合问题. 证明了基于 尾部分布二阶展开的最优投资组合收敛于基于尾部分布一阶展开的最优投资组合. 因此, 对于 V aR 风险度量之下的最优投资组合问题, 如果要求的风险承受水平充分低, 则只需要利用尾 部分布的一阶展开代替厚尾部分布进行近似计算, 就可以达到满意的精度, 从而不需要进行复 杂的高阶运算.     

波动率偏斜与风险中性偏度能预测尾部风险吗

论文从S＆P 500指数期权数据中提取出波动率偏斜与风险中性偏度指标, 采用Logistic模型研究了波动率偏斜/风险中性偏度是否对未来真实的市场尾部风险具有预测力。结果发现, 波动率偏斜/风险中性偏度仅含有未来市场尾部风险的一定信息, 但并不能准确预测未来市场尾部风险发生的状态。相反, 波动率偏斜/风险中性偏度与投资者情绪指标显著相关。     

Limited information likelihood analysis of survey data

Analysts of survey data are often interested in modelling the population process, or superpopulation, that gave rise to a 'target' set of survey variables. An important tool for this is maximum likelihood estimation. A survey is said to provide limited information for such inference if data used in the design of the survey are unavailable to the analyst. In this circumstance, sample inclusion probabilities, which are typically available, provide information which needs to be incorporated into the analysis. We consider the case where these inclusion probabilities can be modelled in terms of a linear combination of the design and target variables, and only sample values of these are available. Strict maximum likelihood estimation of the underlying superpopulation means of these variables appears to be analytically impossible in this case, but an analysis based on approximations to the inclusion probabilities leads to a simple estimator which is a close approximation to the maximum likelihood estimator. In a simulation study, this estimator outperformed several other estimators that are based on approaches suggested in the sampling literature.     

Non‐parametric Estimation of Extreme Risk Measures from Conditional Heavy‐tailed Distributions

In this paper, we introduce a new risk measure, the so‐called conditional tail moment. It is defined as the moment of order a ≥ 0 of the loss distribution above the upper α‐quantile where α ∈ (0,1). Estimating the conditional tail moment permits us to estimate all risk measures based on conditional moments such as conditional tail expectation, conditional value at risk or conditional tail variance. Here, we focus on the estimation of these risk measures in case of extreme losses (where α ↓0 is no longer fixed). It is moreover assumed that the loss distribution is heavy tailed and depends on a covariate. The estimation method thus combines non‐parametric kernel methods with extreme‐value statistics. The asymptotic distribution of the estimators is established, and their finite‐sample behaviour is illustrated both on simulated data and on a real data set of daily rainfalls.     

Ranked set sampling with unequal samples for skew distributions

A ranked set sampling procedure with unequal samples for positively skew distributions (RSSUS) is proposed and used to estimate the population mean. The estimators based on RSSUS are compared with the estimators based on ranked set sampling (RSS) and median ranked set sampling (MRSS) procedures. It is observed that the relative precisions of the estimators based on RSSUS are higher than those of the estimators based on RSS and MRSS procedures.