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本文研究了线性模型响应变量被污染且被区间截断下的参数估计问题, 借助于区间数据的无偏转换, 得到了回归系数和污染系数的估计, 并在一定的条件下得到了这些估计的强相合性. 通过若干模拟例子说明, 尽管数据经过污染和区间截断的双重信息损失, 但用本文提出的方法得到的估计, 仍能取得良好的估计效果     

Some dual characterizations of Farkas-type results for fractional programming problems

In this paper, we present some Farkas-type results for a fractional programming problem. To this end, by using the properties of dualizing parametrization functions, Lagrangian functions and the epigraph of the conjugate functions, we introduce some new notions of regularity conditions and then obtain some dual forms of Farkas-type results for this fractional programming problem. We also obtain sufficient conditions for alternative type theorems. As an application of these results, we obtain the corresponding results for a convex optimization problem.     

A short note on solvability of systems of interval linear equations

In this note we formulate necessary and sufficient conditions for strong solvability and feasibility of systems of linear interval equations in terms of absolute value inequalities.     

Transformations of interval linear systems of equations and inequalities

Very recently, new results on transformation of interval linear systems and on generalizations of the Farkas lemma to interval systems appeared in the literature. They are by far not obvious since the standard transformations on linear systems are not easily adapted to interval system due to the dependency problem. The aim of this paper was to come up with new possible transformations and to extend the results to more general classes of AE interval systems and to linear parametric systems. We also show that the transformations can help in simplifying the proofs of some characterization theorems.     

Direct and iterative methods for interval parametric algebraic systems producing parametric solutions

This paper deals with interval parametric linear systems with general dependencies. Motivated by the so‐called parameterized solution introduced by Kolev, we consider the enclosures of the solution set in a revised affine form. This form is advantageous to a classical interval solution because it enables us to obtain both outer and inner bounds for the parametric solution set and, thus, intervals containing the endpoints of the hull solution, among others. We propose two solution methods, a direct method called the generalized expansion method and an iterative method based on interval‐affine Krawczyk iterations. For the iterative method, we discuss its convergence and show the respective sufficient criterion. For both methods, we perform theoretical and numerical comparisons with some other approaches. The numerical experiments, including also interval parametric linear systems arising in practical problems of structural and electrical engineering, indicate the great usefulness of the proposed methodology and its superiority over most of the existing approaches to solving interval parametric linear systems.     

Regularity conditions characterizing Fenchel–Lagrange duality and Farkas-type results in DC infinite programming

In this paper, we consider a DC infinite programming problem (P) with inequality constraints. By using the properties of the epigraph of the conjugate functions, we introduce some new notions of regularity conditions for (P). Under these new regularity conditions, we completely characterize the Fenchel–Lagrange duality and the stable Fenchel–Lagrange duality for (P). Similarly, we also completely characterize the Farkas-type results and the stable Farkas-type results for (P). As applications, we obtain the corresponding results for conic programming problems.     

一类线性规划问题的区间调节熵算法

本文将熵函数的思想和区间分析相结合,构造了一类线性规划问题的区间调节熵算法,讨论了调节熵函数的区间扩张及其收敛阶,以及相关的区域删除检验原则,证明了算法的收敛性,给出了数值算例.理论与数值结果表明该方法是可靠和有效的.     

基于区间数的证券组合投资模型研究

提出了证券组合投资的区间数线性规划模型.通过引入区间数线性规划问题中的目标函数优化水平α和约束水平β将目标函数和约束条件均为区间数的线性规划问题转化为确定型的线性规划问题.投资者可以根据自己的风险喜好程度和客观情况,对这两个参数做出不同的估计,从而得到相应情况下的有效投资方案,使证券组合投资决策更具柔性.最后通过实例分析说明了该模型的可行性.     

三元区间数线性规划及其解法

在三元区间数理论的基础上,提出了三元区间数线性规划模型的一般形式.利用三元区间数的弱偏好序关系,定义了三元区间数线性规划的弱可行解和弱最优解,并将它的弱最优解转化为求三个一般线性规划模型的最优解,从而在理论上对区间数线性规划进行拓展.最后,通过数值例子对该理论及模型求解方法进行说明和验证.     

Some new Farkas-type results for inequality systems with DC functions

We present some Farkas-type results for inequality systems involving finitely many DC functions. To this end we use the so-called Fenchel-Lagrange duality approach applied to an optimization problem with DC objective function and DC inequality constraints. Some recently obtained Farkas-type results are rediscovered as special cases of our main result.     

含交易费用的证券组合投资模型的满意解

在证券组合投资过程中,忽略交易费用会导致非有效的证券组合投资,本文提出了一个考虑交易费用的证券组合投资的区间数线性规划模型,通过引入区间数线性规划问题中的目标函数优化水平参数λ和约束条件满足水平参数η将目标函数和约束条件均为区间数的区间数线性规划模型转化为确定型的一般线性规划模型,进而求得相应于优化水平λ和满足水平η的满意解.     

Linear interval equations with symmetric solution sets

Criteria for symmetry and boundedness are found for the combined solution set of a system of linear algebraic equations with interval coefficients. It is shown that the problem of the best inner interval estimation of a symmetric solution set can be exactly solved by linear programming methods.     

区间运算和静力区间有限元

用均值和离差两参数表征区间变量的不确定性,根据区间运算规则,论证了区间变量的运算特性.将区间分析和有限元方法相结合,提出了非概率不确定结构的一种区间有限元分析方法.将区间有限元静力控制方程中n自由度不确定位移场特征参数的求解归结为求解一2n阶线性方程组.实例分析表明文中方法是有效和可行的.     

Ⅰ型区间删失情形下部分线性模型Sieve极大似然估计渐近性质

本文在响应变量的观测值为Ⅰ型区间删失数据的情形下,讨论部分线性模型Ｓｉｅｖｅ极大似然估计的渐近性质．在一定条件下证明了该估计具有强相合性;参数分量的估计具有渐近正态性,并且是渐近有效的;非参数分量估计达到了最优弱收敛速度．     

On differential equations with interval coefficients

In this study, a new approach is developed to solve the initial value problem for interval linear differential equations. In the considered problem, the coefficients and the initial values are constant intervals. In the developed approach, there is no need to define a derivative for interval-valued functions. All derivatives used in the approach are classical derivatives of real functions. The reason for this is that the solution of the problem is defined as a bunch of real functions. Such a solution concept is compatible also with the robust stability concept. Sufficient conditions are provided for the solution to be expressed analytically. In addition, on a numerical example, the solution obtained by the proposed approach is compared with the solution obtained by the generalized Hukuhara differentiability. It is shown that the proposed approach gives a new type of solution. The main advantage of the proposed approach is that the solution to the considered interval initial value problem exists and is unique, as in the real case.     

白骨化尸体死亡时间的推断

本文分析了15具白骨化尸体标本的股骨汞(Hg),铅(Pb),镉(Cd)元素含量数据,在三年的时间内采集了3次,一共收集到45个数据。首先将这组数据看着纵向数据,利用线性随机效应混合模型、Cox随机混合效应模型进行分析,结果显示,如果对每个白骨化尸体标本建立线性模型,可以精确预测出死亡时间,而且不需要采集铅元素含量数据。混合效应模型的预测效果也很好,最大误差不会超过1个月。其次我们对数据不作任何假设,利用机器学习中随机森林方法分析数据,并利用5折交叉验证方法来判断结果的可靠性,训练集和测试集的NMSE分别为0.1205944,0.5604286,因此可以用训练出的模型来预测死亡时间。     

解线性互补问题的区间GAOR方法

1引言设M∈Rn×n,q∈Rn,则线性互补问题LCP(M,q)指的是寻找一个向量x∈Rn,使其满足下面的条件: x≥0 Mx+q≥0 xt(Mx+q)=0由于线性互补问题在工程物理、管理学、经济学、约束最优化等领域的应用非常广泛,所以该问题的研究一直倍受大家的关注,至今已有很多有效的算法.早在20世纪80年代     

解一类线性互补问题的区间方法

1引言线性互补问题简记为LCP(M,q)是指对给定的n×n阶实方阵M和N维实向量q,求满足下列条件的实向量x：x≥0,Mx q≥0,(1．1) x~T(Mx q)=0．它在工程物理、管理学、经济学、约束最优化等领域有着广泛的应用背景．备受人们关注     

线性混合模型中方差分量的广义推断

本文考虑了线性混合模型中方差分量的假设检验和区间估计问题.基于广义P-值和广义置信区间的概念,构造了对应于随机效应的单个方差分量的精确检验和置信区间.所构造的广义p-值和广义置信区间是最小充分统计量的函数.对于两个独立线性混合模型中对应于随机效应的方差分量的比较,建立了精确检验和置信区间.进-步,研究了所给检验和置信区间的统计性质,给出了这些检验方法与文献中已有方法的功效比较的模拟结果.模拟结果表明,新检验在功效方面有显著的改进.最后,通过-个实例来演示本文方怯.