搜索一阶交互效应的序贯设计

§1.引言 在用正交表做完一批试验后,经常需要进一步搜索是否存在交互效应和估计这些效应的问题。目前解决这个问题的办法是在假定某些交互效应为零,另一些不为零而后设计试验,这样不仅不合理,而且试验次数较多。本文提出序贯设计的办法,更为合理地搜索那些不为零的交互效应,达到节省试验的目的。 我们将从如下形式的线性模型出发:     

面板数据分位数回归模型求解的模式搜索法

本文应用最优化理论,对固定效应的面板数据分位数回归模型,提出一种模式搜索方法,此方法可以同时估计出所有分位点处的解释变量系数和所有个体的固定效应值。进一步利用蒙特卡洛模拟比较现有文献中涉及的面板数据分位数回归方法,结果显示无论误差项是否满足经典假设,模式搜索分位数回归法较之其他分位数回归估计方法更为有效.     

线性混合效应模型的正交经验似然推断

基于经验似然方法和QR分解技术, 对线性混合效应模型提出了一个基于正交经验似然的估计方法. 在一些正则条件下, 证明了所提出的经验对数似然比函数渐近服从卡方分布, 进而给出了模型固定效应的置信区间估计. 所提出估计过程不受模型随机效应的影响, 进而保证了所给出的估计是比较有效的. 一些数值模拟和实例分析进一步表明了所提出的估计方法是行之有效的.     

含右删失数据的ZIP模型及其应用

零膨胀Poisson回归(ZIP)是处理零频数过多计数资料的有效模型,而计数数据一般含有删失或不精密的特点.本文将删失数据引入到ZIP模型中来,分别建立含右删失数据的固定效应ZIP模型,随机效应ZIP模型,通过极大边际似然函数估计法对模型进行参数估计.最后,利用实例分析验证了上述模型的可行性.     

线性混合效应模型的有效稳健经验似然推断

本文考虑线性混合效应模型的有效稳健经验似然统计推断问题. 通过结合众数回归方法和矩阵的QR分解技术, 提出了一种基于众数回归的正交经验似然统计推断过程. 证明提出的关于固定效应的经验对数似然比函数渐近服从中心卡方分布, 进而构造了模型固定效应的置信区间. 所提出的估计过程不需要对随机效应和模型误差的分布施加任何假定, 并且关于固定效应的估计过程不受随机效应的影响, 因此具有较好的稳健性和有效性.     

黄金分割比与对称截去

本文研究了优选法中一维搜索区间趋于零的充要条件.利用建立的对称截去模型,证明0.618法(优选法)是最快的算法.     

固定效应模型参数估计方法选择的探究

针对固定效应模型的参数估计问题,目前主要有三种估计方法:组内变换法、差分法、虚拟变量法.通过理论分析与蒙特卡洛模拟实验相结合的方法,在模型误差项存在三种自相关情况下,探究了固定效应模型参数估计方法的选择问题.研究发现:①组内变换法与虚拟变量法完全一致;②当模型误差项不存在自相关时,适合选择组内变换法;③当模型误差项服从...     

磁通量子隧道效应及其对实验临界电流的影响

采用磁扫描测量方法,在YBCO(123和124)薄膜上获得了实验临界电流和磁弛豫率随温度及磁场的依赖关系,借助于集体钉扎和热激活磁通运动模型,求出了真实临界电流(即对应于激活能为0的电流),从而区分开量子磁通隧道效应和热激活磁通运动对实验临界电流的影响,发现当温度(T)约低于10K时,由于磁通量子隧道效应的存在使得磁弛豫率不再随温度的下降外延至零,这种额外的磁通运动进一步降低了实验临界电流值,使其在低温下随温度降低而趋于饱和.     

一类具有分布时滞和非局部空间效应的合作模型的稳定性

构造并研究了一类具有分布时滞和非局部空间效应影响的两种群成年个体相互合作的反应扩散模型.利用线性稳定化方法和Redlinger上下解方法得到了该合作模型的动力性态,并证明了模型在零平衡点和边界平衡点是不稳定的,而在正平衡点是全局渐近稳定的.     

考虑空间效应的贝叶斯分层模型与索赔频率预测

在非寿险索赔频率预测中,使用最为广泛的是广义线性模型.但是,如果观察数据呈现出明显的零膨胀特征,或者包含空间协变量,或者某些协变量之间具有分层结构,则广义线性模型的拟合优度往往欠佳.在零膨胀分布假设下,建立了考虑空间效应的贝叶斯分层模型,并将其应用于索赔频率预测.在模型中,用惩罚样条函数描述连续型协变量的非线性效应,用高斯马尔科夫随机场描述相邻地区在索赔频率上的空间相依性,用随机截距项描述不同地区在索赔频率上的分层关系和差异性.实证研究结果表明,考虑空间效应的贝叶斯分层模型的拟合优度明显优于传统的广义线性模型.     

The Poisson random effect model for experience ratemaking: Limitations and alternative solutions

Poisson random effect models with a shared random effect have been widely used in actuarial science for analyzing the number of claims. In particular, the random effect is a key factor in a posteriori risk classification. However, the necessity of the random effect may not be properly assessed due to the dual role of the random effect; it affects both the marginal distribution of the number of claims and the dependence among the numbers of claims obtained from an individual over time. We first show that the score test for the nullity of the variance of the shared random effect can falsely indicate significant dependence among the numbers of claims even though they are independent. To mitigate this problem, we propose to separate the dual role of the random effect by introducing additional random effects to capture the overdispersion part, which are called saturated random effects. In order to circumvent heavy computational issues by the saturated random effects, we choose a gamma distribution for the saturated random effects because it gives the closed form of marginal distribution. In fact, this choice leads to the negative binomial random effect model that has been widely used for the analysis of frequency data. We show that safer conclusions about the a posteriori risk classification can be made based on the negative binomial mixed model under various situations. We also derive the score test as a sufficient condition for the existence of the a posteriori risk classification based on the proposed model.     

紧急网络中的最小饱和流问题

网络N中的一个流,如果沿前向已无法再增流,则称为饱和流,在交通拥挤或紧急疏散时,网络往往被一饱和流所堵塞。显然,这饱和流的值越小,网络的性能就越差。于是从网络分析的观点就提出最小饱和流问题。本文首先证明此问题NP－困难的。然后给出关于最小饱和流与最大流的关系及算法方面的结果。     

INFLUENCE ANALYSIS ON EXPONENTIAL NONLINEAR MODELS WITH RANDOM EFFECTS

This paper presents a unified diagnostic method for exponential nonlinearmodels with random effects based upon the joint likelihood given by Robinson in 1991.The authors show that the case deletion model is equivalent to mean shift outlier model.From this point of view, several diagnostic measures, such as Cook distance, score statistics     

带随机效应非线性模型的影响分析

Abstract. In this paper,a unified diagnostic method for the nonlinear models with random ef-fects based upon the joint likelihood given by Robinson in 1991 is presented. It is shown that thecase deletion model is equivalent to the mean shift outlier model. From this point of view ,sever-al diagnostic measures, such as Cook distance, score statistics are derived. The local influencemeasure of Cook is also presented. A numerical example illustrates that the method is avail-able     

中国股市跨行业动量效应和反转效应研究

动量效应和反转效应是两种重要的金融异象,质疑了有效市场假说。本文以2000～2009年的A股上市公司为研究样本,采用不同的形成期搭配不同的持有期下的投资策略考察了中国股市跨行业动量效应和反转效应。研究结论表明:在沪深A股市场,按下游行业收益率排序的零投资策略主要表现为动量效应,按上游行业收益率排序的零投资策略主要表现为反转效应。从短期来看,跨行业动量或反转效应普遍不显著。持有期中长时,结果的显著性明显提高。跨行业动量或反转效应通过CAPM、Fama-French、Carhart模型调整后仍然显著。     

Bifurcations of an epidemic model with non-monotonic incidence rate of saturated mass action

In this paper, we study the bifurcations of an epidemic model with non-monotonic incidence rate of saturated mass action, which describes the psychological effects of the community on certain serious diseases when the number of infective is getting larger. By carrying out the bifurcation analysis of the model, we show that there exist some values of the model parameters such that numerous kinds of bifurcation occur for the model, such as Hopf bifurcation, Bogdanov–Takens bifurcation.     

A Galois correspondence for countable short recursively saturated models of PA

In this paper we investigate the properties of automorphism groups of countable short recursively saturated models of arithmetic. In particular, we show that Kaye's Theorem concerning the closed normal subgroups of automorphism groups of countable recursively saturated models of arithmetic applies to automorphism groups of countable short recursively saturated models as well. That is, the closed normal subgroups of the automorphism group of a countable short recursively saturated model of PA are exactly the stabilizers of the invariant cuts of the model which are closed under exponentiation. This Galois correspondence is used to show that there are countable short recursively saturated models of arithmetic whose automorphism groups are not isomorphic as topological groups. Moreover, we show that the automorphism groups of countable short arithmetically saturated models of PA are not topologically isomorphic to the automorphism groups of countable short recursively saturated models of PA which are not short arithmetically saturated (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

具有时变协变量的纵向资料的线性混合效应模型及算法

许多研究领域中都会涉及到纵向资料的分析处理.在纵向资料的分析中,常常遇到带有时变协变量的情况.传统的方差分析难以处理具有时变协变量的纵向资料.对线性混合效应模型应用于分析这类资料进行了方法学的探讨,并编制了模型拟合的SAS程序.通过实例应用,对线性混合效应模型分析纵向资料的方法和过程给出详细的介绍.     

Single-machine group scheduling with general deterioration and learning effects

In this paper we consider single-machine group scheduling problems with effects of learning and deterioration at the same time. By effects of learning and deterioration, we mean that the group setup times are general linear functions of their starting times and the jobs in the same group have general position-dependent and time-dependent learning effects. The objective of scheduling problems is to minimize the makespan and the sum of completion times, respectively. We show that the problems remain solvable in polynomial time under the proposed model.