基于熵测度的三参数区间数信息下的TOPSIS决策方法

研究基于三参数区间数的排序及决策模型,提出了基于三参数区间数的重心点、中点、长度的可能度排序方法;基于重心点发生可能性最大的三参数区间数分布特点,提出了距离测度公式;建立了基于三参数区间数熵测度的属性权重模型,在此基础上构建了依据TOPSIS思想的不确定性决策框架。算例说明了该方法的步骤和有效性。     

基于决策者满意度的区间DEA的求解

定义了一种反映决策者满意度的区间数序关系,基于此将区间DEA中的区间不等式约束转化为确定型约束。研究了区间DEA模型向确定型DEA模型转化过程中的数据一致性问题。在保持数据一致性的前提下,根据决策者给出的满意度水平,将区间DEA转化为确定型DEA并进行求解。最后给出算例,并总结和分析了决策单元的DEA效率值随满意度水平变化的规律。     

Inference on Regressions with Interval Data on a Regressor or Outcome

This paper examines inference on regressions when interval data are available on one variable, the other variables being measured precisely. Let a population be characterized by a distribution P(y, x, v, v₀, v₁), where y∈R¹, x∈R^k, and the real variables (v, v₀, v₁) satisfy v₀≤v≤v₁. Let a random sample be drawn from P and the realizations of (y, x, v₀, v₁) be observed, but not those of v. The problem of interest may be to infer E(y|x, v) or E(v|x). This analysis maintains Interval (I), Monotonicity (M), and Mean Independence (MI) assumptions: (I) P(v₀≤v≤v₁)=1; (M) E(y|x, v) is monotone in v; (MI) E(y|x, v, v₀, v₁)=E(y|x, v). No restrictions are imposed on the distribution of the unobserved values of v within the observed intervals [v₀, v₁]. It is found that the IMMI Assumptions alone imply simple nonparametric bounds on E(y|x, v) and E(v|x). These assumptions invoked when y is binary and combined with a semiparametric binary regression model yield an identification region for the parameters that may be estimated consistently by a modified maximum score (MMS) method. The IMMI assumptions combined with a parametric model for E(y|x, v) or E(v|x) yield an identification region that may be estimated consistently by a modified minimum‐distance (MMD) method. Monte Carlo methods are used to characterize the finite‐sample performance of these estimators. Empirical case studies are performed using interval wealth data in the Health and Retirement Study and interval income data in the Current Population Survey.     

Exact uniformly most powerful postselection confidence distributions

A conditioning on the event of having selected one model from a set of possibly misspecified normal linear regression models leads to the construction of uniformly optimal conditional confidence distributions. They can be used for valid postselection inference. The constructed conditional confidence distributions are finite sample exact and encompass all information regarding the focus parameter in the selected model. This includes the construction of optimal postselection confidence intervals at all significance levels and uniformly most powerful hypothesis tests.     

基于区间灰作用量的GM(1,1)均值差分模型解的非唯一性研究

GM(1,1)是结构信息不完全的灰色预测模型，但当前其模拟及预测结果的实数形式不满足灰色理论解的非唯一性原理。文章从GM(1,1)网络模型出发，分析了灰作用量的背景与内涵，还原了影响因素不确定条件下灰作用量的区间灰数形式，构建了具有非唯一解的新型GM(1,1)均值差分模型。新模型具有更加完善的体系结构，同时能实现对传统 GM(1,1)均值差分模型的完全兼容。应用新模型对我国电力能源消费量进行建模，结果显示其建模结果的合理性优于传统 GM(1,1)模型。本研究成果对丰富灰色预测模型理论框架、完善灰色预测模型结构体系具有积极意义。     

基于新型核与灰度序列的MGM(1,m,N)模型及其应用

雾霾是空气质量重要评判标准之一，对其进行准确预测能为相关政府部门及时做出正确决策提供理论支持，因此预测雾霾具有实际意义。本文针对区间灰数分布信息已知的序列，构建多个影响因素作用于多个系统行为变量的灰色MGM(1,m,N)模型。首先根据可能度函数计算得到区间灰数的新型核与灰度序列，然后对新型核与灰度序列分别建立MGM(1,m,N)模型以求得模拟值和预测值，最后通过还原得到区间灰数序列的上、下界。为进一步验证该模型的可行性，本文将该模型应用于雾霾相关数据并与基于传统核与灰度序列的MGM(1,m,N)模型进行比较，结果表明本文构建的新模型的模拟预测精度都较传统模型更好。     

基于改进自适应最优分割法的风险预警区间模型研究——针对重大突发公共卫生事件

重大突发公共卫生事件，譬如新型冠状病毒疫情，严重危害着世界各国人民的生命安全，风险预警是构建重大突发公共卫生事件风险预警管控体系的关键所在，而其风险预警区间的精准确定是关乎预警等级的关键问题。基于自适应最优分割模型，引入熵值法计算各指标权重，采用多种函数拟合识别函数特征，构建了改进的自适应最优分割模型，定量科学划分了重大突发公共卫生事件风险预警区间。通过结合实际案例，应用Matlab软件进行仿真，验证了预警区间的吻合度，为构建重大突发公共卫生事件风险预警防控提供了理论参考。     

An improved score-type confidence interval for stratified risk differences involving rare events

A stratified analysis of the differences in proportions has been widely employed in epidemiological research, social sciences, and drug development. It provides a useful framework for combining data across strata to produce a common effect. However, for rare events with incidence rates close to zero, popular confidence intervals for risk differences in a stratified analysis may not have appropriate coverage probabilities that approach the nominal confidence levels and the algorithms may fail to produce a valid confidence interval because of zero events in both the arms of a stratum. The main objective of this study is to evaluate the performance of certain methods commonly employed to construct confidence intervals for stratified risk differences when the response probabilities are close to a boundary value of zero or one. Additionally, we propose an improved stratified Miettinen–Nurminen confidence interval that exhibits a superior performance over standard methods while avoiding computational difficulties involving rare events. The proposed method can also be employed when the response probabilities are close to one.     

Nonparametric asymptotic confidence intervals for extreme quantiles

In this paper, we propose new asymptotic confidence intervals for extreme quantiles, that is, for quantiles located outside the range of the available data. We restrict ourselves to the situation where the underlying distribution is heavy-tailed. While asymptotic confidence intervals are mostly constructed around a pivotal quantity, we consider here an alternative approach based on the distribution of order statistics sampled from a uniform distribution. The convergence of the coverage probability to the nominal one is established under a classical second-order condition. The finite sample behavior is also examined and our methodology is applied to a real dataset.