一阶回归模型下Q和Q_B准则的几个结果

在试验设计中,一阶回归模型通常被作为合格拟合模型用来从众多因子中筛选出效应显著的特殊因子,而Q和Q_B准则能够比较简单地从大量的合格拟合模型中找出具有最优性质的设计.主要探讨了当拟合模型为一阶回归模型时,二水平的初始设计d与其Double设计(d d d -d)在Q和Q_B准则下的最优关系.给出了初始设计d的Q和Q_B值与其Double设计的Q和Q_B值之间的解析关系,从而得到在Q或Q_B准则下如果初始设计d是最优的,那么其Double设计也是最优的.此外,也分别给出了初始设计d及其Double设计的Q值和Q_B值的一个下界.     

Q准则下的最优double设计

最近,Q准则被用来研究设计在模型未知前提下的投影效率,并用它作为因子筛选准则来筛选最优的设计.本文里,我们将讨论double设计D(d)与其初始设计d的Q准则之间的联系.     

自协方差非平稳时间序列的时变参数自回归模型

对一簇时间序列明确定义了自协方差非平稳时间序列.对于自协方差非平稳时间序列,提出了用于自协方差非平稳时间序列的3种时变参数自回归（TVPAR）模型：满阶TVPAR模型、非时变阶次TVPAR模型和时变阶次TVPAR模型.并进行了有关的最小赤池信息量准则（AIC）估计.     

一阶自回归模型参数变点的假设检验

本文讨论一阶自回归模型自回归参数$\phi$的变点问题. 对于一阶自回归模型, 在模型的白噪声序列的方差$\sigma^2$已知和未知的条件下, 利用最大似然方法, 我们分别讨论了模型自回归参数$\phi$的Abrupt Change-Point 和Gradual Change-Point的检测问题.     

固定设计与随机设计下模型选择的简单方法及其相合性研究

本文研究了固定设计和随机设计下线性回归模型的选择问题,建立了两种模型通用的选择准则,该准则计算简单,并且在一定的条件下具有强相合性.     

线性回归系数最小二乘估计弱相合性的一个结果

假定线性回归模型的误差列为i.i.d.,有r阶矩,1≤r＜2.[1]中证明若     

随机回归模型选择的简单方法及其相合性

随机回归模型的选择是回归分析理论中的重要问题之一.本文对随机回归模型提供一种选择准则,它的计算简单,在一定的条件下,该准则具有强相合性.     

关于Q(√/4k2x+1)的理想类群的循环子群

设d,a,k,n是适合4k2n+1 =da2, k>1, n>2, d无平方因子的正整数;又设C(K)和h(K)分别是实二次域K=Q(√d)的理想类群和类数.本文证明了:当a<0.5k0.56n时,则h(K)≡0(mod n)和C(K)必有n阶循环子群.     

回归模型的最佳变量子集合选择

本文在信息量准则的基础上着重从两个方面来阐述回归模型的最佳变量子集合选择方法:1.主成分分析方法选取主因子,以降低维数;2.主成分分析倒筛法和信息量准则相结合.文中以实例着重阐述如何运用第二种方法,得到了满意的选择效果.本方法在理论上是严谨的,实际上是可行的.     

对《烟卷需求预测分析》一文中的一阶自回归模型的一点意见

《数理统计与管理》1985年第2期刊登了厉无畏、陈漪清二同志的《我国卷烟需求预测分析》一文。该文第一节“短期预测”似有商榷必要。该文用一阶自回归模型进行预测,并用最小二乘法估计系数得:剩余标准差S=59.3,相关系数0.9.85.但是从作者提供的数据看,虽然样本量n不大,却已明显地表现出一种增长趋势(图1).将它作为平稳数列处理虽然是不妥当的.较好的办法是进行一阶差分处理,经过一阶差分后的数列比较地说有平稳性了(图2).我们仍用AR(0,p)来模拟卷烟供应情况,并用它对未来的销售趋势进行于测,用AIC准则确定自回归模型的阶数,现把计算结果…     

Optimal control problem of the uncertain second‐order circuit based on first hitting criteria

First hitting criteria of a system are to initially achieve some performance indeces of the target state set. This paper primarily investigates the optimal control problem of the uncertain second‐order circuit based on first hitting criteria. First, considering time efficiency and different from the ordinary expected utility criterion over an infinite time horizon, two first hitting criteria which are reliability index and reliable time criteria are innovatively proposed. Second, assuming the circuit output voltage as an uncertain variable when the historical data is lacking, we better model the real circuit system with the uncertain second‐order differential equation which is essentially the uncertain fractional‐order differential equation. Then, based on the first hitting time theorem of the uncertain fractional‐order differential equation, the distribution function of the first hitting time under the second‐order circuit system is proposed and the uncertain second‐order circuit optimal control model (reliability index and reliable time‐based model) is transformed into corresponding crisp optimal problem. Lastly, analytic expressions of the optimal control for the reliability index model are obtained. Meanwhile, sufficient condition and guidance for parameters for the optimal solution of the reliable time‐based model are derived, and corresponding numerical examples are also given to demonstrate the fluctuation of our optimal solution for different parameters.     

On stopped decision processes with discrete time parameter

A non-stationary stopped decision process is investigated under rather weak convergence assumptions on the expected total rewards. Sufficient conditions are given for the approximation of the maximal conditional expected rewards from infinite stage play by the maximal conditional expected rewards from finite stage play. General criteria of optimality are derived. The results are essentially based on two lemmas given in this paper. The existence of optimal plans is established using results of non-stationary dynamic programming.     

判定二阶线性矩阵微分系统振动性的新准则

利用一个线性变换给出了二阶矩陈微分系统(P(t)X′(t))′+Q(t)X(t)=0 t∈[t_0,∞)的振动性的新的判定准则,从而推广和改进了前人的结论.     

二阶矩阵微分系统的区间振动准则

本文利用矩阵Riccati技巧,平均技巧及矩阵不等式,建立形如[P(t)Y']' Q(t)Y=0的二阶矩 阵微分系统的一些新的区间振动准则.所得结果推广,改进和包含一系列已有的结论,并能应用于已知 准则不能适用的若干情形.     

研究生招生规模、教育质量和就业率的三维非线性动力学模型分析

考虑研究生招生规模、教育质量和就业率3者之间的相互影响关系,建立了三维非线性动力学模型,利用Routh-Hurwitz判别准则和稳定性判别法给出了模型平衡点的稳定性条件,确定了研究生的最优招生规模。     

Optimization of structural design

Typical problems of optimal structural design are discussed to indicate mathematical techniques used in this field. An introductory example (Section 2) concerns the design of a beam for prescribed maximal deflection and shows how suitable discretization may lead to a problem of nonlinear programming, in this case, convex programming. The problem of optimal layout of a truss (Section 3) is discussed at some length. A new method of establishing optimality criteria (Section 4) is illustrated by the optimal design of a statically indeterminate beam of segmentwise constant or continuously varying cross section for given deflection under a single concentrated load. Other applications of this method (Section 5) are briefly discussed, and a simple example of multipurpose design (Section 6) concludes the paper.     

An algorithm for solving a multiple criteria optimal control problem

An algorithm for finding agood solution for a multiple criteria optimal control problem is given. The criteria are assumed to be ordered according to their importance to the decision-maker. The algorithm consists of successive solutions of single criterion optimal control problems. Other criteria are taken into account by adding constraints to the problem in a systematic manner.     

Linear transformation and oscillation criteria for Hamiltonian systems

Using a linear transformation similar to the Kummer transformation, some new oscillation criteria for linear Hamiltonian systems are established. These results generalize and improve the oscillation criteria due to I.S. Kumari and S. Umanaheswaram [I. Sowjaya Kumari, S. Umanaheswaram, Oscillation criteria for linear matrix Hamiltonian systems, J. Differential Equations 165 (2000) 174-198], Q. Yang et al. [Q. Yang, R. Mathsen, S. Zhu, Oscillation theorems for self-adjoint matrix Hamiltonian systems, J. Differential Equations 190 (2003) 306-329], and S. Chen and Z. Zheng [Shaozhu Chen, Zhaowen Zheng, Oscillation criteria of Yan type for linear Hamiltonian systems, Comput. Math. Appl. 46 (2003) 855-862]. These criteria also unify many of known criteria in literature and simplify the proofs.     

Bayesian planning of step‐stress accelerated degradation tests under various optimality criteria

Step‐stress accelerated degradation testing (SSADT) has become a common approach to predicting lifetime for highly reliable products that are unlikely to fail in a reasonable time under use conditions or even elevated stress conditions. In literature, the planning of SSADT has been widely investigated for stochastic degradation processes, such as Wiener processes and gamma processes. In this paper, we model the optimal SSADT planning problem from a Bayesian perspective and optimize test plans by determining both stress levels and the allocation of inspections. Large‐sample approximation is used to derive the asymptotic Bayesian utility functions under 3 planning criteria. A revisited LED lamp example is presented to illustrate our method. The comparison with optimal plans from previous studies demonstrates the necessity of considering the stress levels and inspection allocations simultaneously.     

Asset Allocation and Reinsurance Policy for a Mean-Variance-CVaR Insurer in Continuous-Time

This paper studies the optimal asset allocation and reinsurance problem under mean-variance-CVaR criteria for an insurer in continuous-time. We obtain the closed-form solution of optimization problem by using martingale method. Numerical results show the trends of optimal wealth, investment and reinsurance strategies with various parameter values.