Continuous opinion model in small-world directed networks

In the compromise model of continuous opinions proposed by Deffuant et al., the states of two agents in a network can start to converge if they are neighbors and if their opinions are sufficiently close to each other, below a given threshold of tolerance ?. In directed networks, if agent i is a neighbor of agent j,j need not be a neighbor of i. In Watts-Strogatz networks we performed simulations to find the averaged number of final opinions 〈F〉 and their distribution as a function of ? and of the network structural disorder. In directed networks 〈F〉 exhibits a rich structure, being larger than in undirected networks for higher values of ?, and smaller for lower values of ?.     

Bartlett分解与多元正态总体均值的广义推断

对多个正态总体均值的统计推断是一个古老而令人感兴趣的问题.本文利用样本协方差矩阵的Bartlett分解和广义p-值的概念给出一些关于均值的精确检验.模拟显示这些检验比已有的检验有更高的功效.同时,还根据协方差矩阵的Bartlett分解和样本均值向量,得到一个分布和未知参数无关的统计量,用它可以对多个正态总体共同均值做精确检验.模拟显示,这些检验犯第一错误的概率小于显著性水平,而且有更高的检验功效.     

分数填补下两非参数总体一般差异的经验似然置信区间

在一定的条件下证明了缺失数据情形基于分数填补方法得到的两非参数总体一般差异指标的经验似然比统计量的渐近分布为加权χ21,由此可构造差异指标的经验似然置信区间.     

纵向数据单指标模型中参数的经验似然置信域

考虑纵向数据单指标模型,针对纵向数据组间独立的特点,提出了模型中未知参数的三种经验对数似然比统计量.在适当条件下,证明了所提出的统计量依分布收敛于x~2分布,所得结果可以构造未知参数的置信域.进一步证明了所提出的纠偏的经验对数似然比有许多优良的性质.通过模拟研究对所提方法进行了说明.     

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本文利用广义p值和广义置信区间的概念构造含有三个随机效应的Panel数据模型中方差分量的几种新的精确检验和置信区间,并讨论它们在尺度变换下的不变性.通过模拟给出检验的功效和置信区间的覆盖率. 模拟结果表明,广义p值理论方法应用于含有冗余参数的Panel数据模型参数检验问题是灵活而有效的.     

随机插补下两线性模型中响应变量分位数差异的经验似然置信区间

设两个样本数据不完全的线性模型,其中协变量的观测值不缺失,响应变量的观测值随机缺失。采用随机回归插补法对响应变量的缺失值进行补足,得到两个线性回归模型的"完全"样本数据,在一定条件下得到两响应变量分位数差异的对数经验似然比统计量的极限分布为加权x_1~2,并利用此结果构造分位数差异的经验似然置信区间。模拟结果表明在随机插补下得到的置信区间具有较高的覆盖精度。     

Bootstrap approximation of wavelet estimates in a semiparametric regression model

The inference for the parameters in a semiparametric regression model is studied by using the wavelet and the bootstrap methods. The bootstrap statistics are constructed by using Efron＇s resampling technique, and the strong uniform convergence of the bootstrap approximation is proved. Our results can be used to construct the large sample confidence intervals for the parameters of interest. A simulation study is conducted to evaluate the finite-sample performance of the bootstrap method and to compare it with the normal approximation-based method.     

二项分布的参数估计问题研究

本文主要讨论二项分布的参数估计问题.对GB/T 4087.1-1983,GB/T 4087.2-1983,GB/T4087.3-1985给出的经典二项分布参数点估计、区间估计和可靠度置信下限计算方法进行了分析,指出了其中存在的问题.根据二项分布的数学表达式推导出了二项分布参数的概率分布密度函数,在此基础上提出了进行二项分布参数估计的一般方法.     

Sample size for the Z test and its confidence interval

The statistical power of a significance test is closely related to the length of the confidence interval (i.e. estimate precision). In the case of a Z test, the length of the confidence interval can be expressed as a function of the statistical power.     

Comparing confidence limits for short-run process incapability index Cpp

Process incapability index C_pp has been proposed in the manufacturing industry to assess process incapability. In industries it is sometimes unable to get large samples, and, hence, the CAN (consistent and asymptotically normal) property of the unbiased estimator for C_pp is missing. In this paper, six bootstrap methods are applied to construct upper confidence bounds (UCBs) of C_pp for short-urn production processes where sample size is small; standard bootstrap (SB), Bayesian bootstrap (BB), bootstrap pivotal (BP), percentile bootstrap (PB), bias-corrected percentile bootstrap (BCPB), and bias-corrected and accelerated bootstrap (BCa). A numerical simulation study is conducted in order to demonstrate the performance of the six various estimation methods. We further investigate the accuracy of the six methods by calculating the relative coverage (defined as the ratio of coverage percentage to average length of UCB). Detailed discussions of simulation results for seven short-run processes are presented. Finally, one real example from Ford Company’s Windsor Casting Plant is used to illustrate the six interval estimation methods.