随机权函数半参数回归模型的导方差统计分析

在回归分析中,观测值的方差齐性只是一个基本的假定,在参数、半参数和非参数回归模型中关于异方差检验和估计问题已有很多研究.本文在冉昊和朱忠义(2004)讨论的半参数回归模型的基础上,用随机参数方法,讨论随机权函数半参数回归模型中的异方差检验问题,得到了方差齐性检验Score统计量,同时,当半参数模型存在异方差时,本文还给出了估计方差的方法.     

线性约束下异方差回归模型参数的极大似然估计

运用参数的极大似然估计法,给出在线性约束条件Hβ=C下异方差回归模型参数β和λ的极大似然估计,并讨论了估计参数的性质和模型的残差.利用得到的结论对线性约束下异方差回归模型的进一步研究和应用具有一定的理论和实际价值.     

响应变量随机缺失下的半参变系数模型的均值估计

在响应变量随机缺失时,研究了半参数变系数模型响应变量均值的借补估计.首先利用完整个体估计模型中的参数与非参数部分,然后再用借补方法与加权借补方法估计响应变量的均值.最后求出了估计的渐近偏差与渐近方差,研究了所得到的估计的渐近性质,并进行模拟比较.     

部分线性变系数模型中估计的渐进正态性

作为部分线性模型与变系数模型的推广,部分线性变系数模型是一类应用非常广泛的模型,本文基于Profile最小二乘方法给出了模型中参数分量与非参数分量的估计,并在异方差情形下证明了这些估计的渐进正态性.     

二元极值分布混合模型的矩估计

极值理论在各个领域得到了越来越多的关注和应用, 尤其是多元极值分布. 而矩估计是一种经典的参数估计方法, 计算简单且具有某些优良性, 本文给出边缘为标准指数分布的二元极值混合模型相关参数的矩估计及其渐近方差. 并将其与极大似然估计的渐近方差比较, 结果表明矩估计是一个较好的估计.     

半参数可加模型的广义Liu估计

作为部分线性模型和可加模型的推广,半参数可加模型在统计建模中应用广泛.考虑这类半参数模型在线性部分自变量存在共线性时的估计问题.基于Profile最小二乘方法,提出了参数分量的广义Profile-Liu估计,并给出了该估计量的偏和方差以及均方误差.最后利用数值模拟验证了所提方法的有效性.     

左截断右删失数据下半参数模型风险率函数估计

文章给出了右删失左截断数据半参数模型下的风险率函数估计,讨论了风险率函数估计的渐近性质,获得了这些估计的渐近正态性,对数律和重对数律.由于假定删失机制服从半参数模型下,从而知道模型的更多信息,因此对于给出参数的极大似然估计,可以改进风险率函数估计的渐近性质.也就是说,删失数据模型具有半参数的辅助信息下, 风险率函数估计的渐近方差比通常的完全非参数的估计的渐近方差更小.这说明加入了额外的信息提高了风险率函数估计的效率.     

方差分量模型参数的广义岭估计

本文先将方差分量模型的方差分量化为派生模型的均值参数，分别作出其相对于ＬＳＥ和ＢＬＵＥ的广义岭估计，再根据二步估计法作出原模型均值参数的广义二乘估计及其进行一步的岭估计。证明了这样不仅使方差分量估计的均方误差减少，而且使原模型均值参数估计的均方误差也不均加和地一步减少。本文还找到了岭参数仅仅依据于样本的估计，这样既将岭估计方法推进至方差分量模型，也改进了方差分量模型参数的离差均值对应方法。     

AR(p)模型中的变点分析

本文分别用极大似然法和Bayes方法研究了AR(p)模型中的变点问题.在数据矩阵不一定满秩的条件下,利用Moore-Penrose广义逆给出了模型参数的极大似然估计的统一表达式和变点位置的估计式.在假定自回归系数的先验分布服从多元正态,方差服从逆Γ分布的条件下,用Bayes方法给出了变点位置估计的显示表达式以及模型参数的Bayes估计.     

部分线性自回归模型中误差方差的核估计

基于非参数函数的核估计,构造了部分线性自回归模型中误差四阶矩的相合估计,从而给出了误差方差核估计的渐近正态性,并通过模拟算例和实例说明了其应用.     

A Nussbaum gain adaptive synchronization of a new hyperchaotic system with input uncertainties and unknown parameters

The sign of unknown input coefficients is assumed to be known in most papers about the input uncertainties. In this paper, a Nussbaum gain method is adopted to cope with the situation that both the sign and the value of input are unknown. And the unknown parameters can be estimated under the situation of unknown sign of control. The synchronization is achieved for a class of hyperchaotic systems with unknown parameters and input uncertainties by adopting of the Nussbaum gain method and the global terminal adaptive method. And the conclusions are made as follows: First, the proposed method is effective in the situation that the sign of input is unknown. Second, the estimation of unknown parameters can be achieved only when the number of unknown parameters satisfied some condition and no uncertainty exist in the input of systems. Third, the unknown parameters cannot be estimated correctly with common adaptive method when there are input uncertainties in the system. But the Nussbaum gain method can get good result in the estimation of unknown parameters. At last, numerical simulations are done to show the effectiveness of the proposed method.     

SARS流行病传染动力学模型

建立了 SARS流行病的数学模型 ,根据部分国家和地区的 SARS疫情数据 ,计算出其模型参数 ,给出了各地 SARS疫情与模拟结果的比较图 ,模拟结果与实际疫情十分吻合 .分析了 SARS流行特征 ,并对疫情发展进行了预测 .     

Comparison of fuzzy and crisp systems via system dynamics simulation

This paper compares fuzzy and classical decision rules. The hypothesis of this paper is that whether one of these rules is superior depends on the situation. For that comparison the paper uses system dynamics (SD), which models the behavior of systems including human beings. This comparison was made for a simple heating system that is controlled by a human operator. Under various changes of external and internal parameters, the results are that the major differences between fuzzy and crisp systems emerge at extreme values of these parameters. In conclusion, the superiority of crisp rules or fuzzy rules in a decision-making environment depends on the situation.     

Two stage regression model with constraints; admissible second stage parameter estimation

If a regression experiment is realized in two stages, then two possibilities can occur in the second stage. Estimates of the first stage parameters either may be corrected by use of second stage measurements or they must stay unchanged. In the latter case, this requirement must be taken into account when estimating the second stage parameters. The situation is a little more complicated when constraints on both groups of parameters are imposed.     

How do commission rates influence a firm’s success? statistical analysis of a corporate strategy simulation experiment

The purpose of this paper is to analyse the relationship between commission rates and a firm’s success within a corporate strategic planning simulation experiment. Teams of students are assigned to the role of managers of a firm within a competitive market situation. They have the task to experience the complex situation in which they act as managers to increase the performance of a firm by setting specific parameters. Our most interesting parameter is the commission rate. The Marketing Game considers a reasonably complex and realistic situation for the participants. We examine to what extent subjects succeed in increasing a firm’s turnover and profit by varying the commission rates.     

Practical Inventory Replenishment Policies for a Linear Trend in Demand Followed by a Period of Steady Demand

Inventory policies are considered for the situation of a deterministic linear trend in demand followed by a period of constant demand: an idealised form of a common situation in spares provisioning. An analytic optimal solution is derived and its practical shortcomings discussed. The performance of practical inventory policies for this situation are compared and a policy based on the well known economic batch quantity, suitably modified for linear trend, is shown to give small cost penalties when compared to the analytic solution. The good performance of the policy based on the economic batch quantity is maintained, even when used on examples which simulate situations where the parameters of demand are not known exactly. Indeed the method is then superior to all others tried, including the "optimal" analytic method.     

参数具有序限制的统计推断——一个新方法及其在生物统计中的应用

本文绘出参数具有序限制统计推断的一个新方法，并给出了应用实例．此方法可广泛应用于药物发展，公共卫生健康统计及工业质量控制中．     

Parameter cascades and profiling in functional data analysis

A data smoothing method is described where the roughness penalty depends on a parameter that must be estimated from the data. Three levels of parameters are involved in this situation: Local parameters are the coefficients of the basis function expansion defining the smooth, global parameters define low-dimensional trend and the roughness penalty, and a complexity parameter controls the amount of roughness in the smooth. By defining local parameters as regularized functions of global parameters, and global parameters in turn as functions of complexity parameter, we define a parameter cascade, and show that the accompanying multi-criterion optimization problem leads to good estimates of all levels of parameters and their precisions. The approach is illustrated with real and simulated data, and this application is a prototype for a wide range of problems involving nuisance or local parameters.     

威布尔分布组与删失数据下最大似然估计的存在性

本文研究寿命服从威布尔分布,观测数据分组与可能删失的情况下,最大似然估计的存在性,针对所有数据类型,我们给出了最大似然估计存在性的一个充分必要条件,文章结尾讨论了仅一个失效数据时最大似然估计的计算。     

椭球不确定集下具有消费的投资组合鲁棒优化模型

针对含有不确定参数的优化问题,鲁棒优化作为一种有效的优化手段引起了人们的普遍关注。本文主要介绍了CVaR风险投资纽合模型,并在模型中加入消费,将椭球不确定集下鲁棒优化应用到该模型中,这不仅解决了该模型由于参数的不确定性所造成的缺陷,而且也比较符合实际情况。