基于Bootstrap方法的统计分析

Bootstrap方法(也称自助法)是非参数统计中一种非常重要的统计方法.这种方法是将从样本中抽样得到的子样本看作样本,每一次抽出子样本后,计算一次统计量的观测值.通过反复抽样,可得到许多的统计量观测值.进一步可获得统计量的经验分布,然后进行统计推断.并举例说明了在Bootstrap方法下均值与方差的区间估计以及Bootstrap方法的均值的假设检验.     

M/G/c排队系统中顾客队长排队长的置信区间的Bootstrap估计

研究了M/G/c排队系统中顾客队长、排队长的置信区间的求解方法.利用Bootstrap原理,给出了正态区间法、枢轴量法和百分位区间法等三种计算方法.实际应用表明,三种方法都得到了较好的结果.以置信区间的长度为评价标准,正态区间法和百分位区间法较优.     

基于Bootstrap法的核估计逼近

从分布密度函数为f的总体中抽取独立同分布的样本X1,…,Xn,μ=EX1研究密度泛函θ=f(μ)的核型估计fn()的Bootstrap逼近问题.     

正态总体方差和标准差的无偏估计

在正态总体分布下,给出了方差及标准差的矩估计量和极大似然估计量,讨论了两者之间的关系,得出两类估计量相同,并进一步给出无偏估计量。     

双参数指数分布参数的最短置信区间

在双参数指数分布的两个参数的区间估计的基础上,利用Lagrange乘子法和函数单调性得到了各参数的最短置信区间的唯一存在性,给出了各参数最短置信区间的表达式及其等距搜索算法.     

偏态分布下多维测验合成信度区间估计的比较

用合成信度能比α系数更准确地估计测验的合成信度。本文用模拟研究比较了两种估计多维测验合成信度置信区间的方法,结果发现用Delta法通过近似计算得到的标准误,与Bootstrap法的结果差别很小,而且比Bootstrap法简单得多,因此推荐使用Delta法估计多维测验合成信度的置信区间。     

区间估计与假设检验的相关性及应用

对统计推断理论中区间估计与假设检验的区别与联系进行了分析，讨论了两者之间的相关性，给出了利用置信区间解决假设检验问题拒绝域的一种新思路．     

置信区间和置信概率的图解法及在风险投资分析中的应用

风险是在一定条件下和一定时期内可能发生的各种结果的变动程度。财务活动经常是在有风险的情况下进行的。风险大，报酬高；报酬低，风险小。如何进行投资决策，取决于投资人对风险的态度。本对置信区间和置信概率的计算方法用图解的形式进行了分析和探讨，并对其在风险投资分析中的具体运用进行了实证分析。     

Bootstrap框架在响应式Web设计中的应用

Bootstrap是响应式网页设计的主要前端框架。分析了Bootstrap框架的全局CSS栅格系统容器及断点设置对页面布局自适应能力的影响,并以此为基础设计了能适应多尺寸屏幕及分辨率的响应式网站,实现了移动端与 PC 端网页显示的一致性。     

谈统计方法在教学评估中的应用

本文主要是通过对学生学习成绩的统计分析，介绍了正态分布理论，Ｘ~２拟合优度检验法在教学评估中的具体运用．     

非参数bootstrap方法及其MATLAB实现

介绍非参数bootstrap方法的实现步骤,并通过具体实例,利用MATLAB强大的编程和计算功能实现了非参数bootstrap方法。     

Standardized Parameters in Misspecified Structural Equation Models: Empirical Performance in Point Estimates,Standard Errors,and Confidence Intervals

In practice, models always have misfit, and it is not well known in what situations methods that provide point estimates, standard errors (SEs), or confidence intervals (CIs) of standardized structural equation modeling (SEM) parameters are trustworthy. In this article we carried out simulations to evaluate the empirical performance of currently available methods. We studied maximum likelihood point estimates, as well as SE estimators based on the delta method, nonparametric bootstrap (NP-B), and semiparametric bootstrap (SP-B). For CIs we studied Wald CI based on delta, and percentile and BC_a intervals based on NP-B and SP-B. We conducted simulation studies using both confirmatory factor analysis and SEM models. Depending on (a) whether point estimate, SE, or CI is of interest; (b) amount of model misfit; (c) sample size; and (d) model complexity, different methods can be the one that renders best performance. Based on the simulation results, we discuss how to choose proper methods in practice.     

Confidence Intervals for a Semiparametric Approach to Modeling Nonlinear Relations among Latent Variables

Compared to parametric models, nonparametric and semiparametric approaches to modeling nonlinearity between latent variables have the advantage of recovering global relationships of unknown functional form. Bauer (2005) Bauer, D. J. 2005. A semiparametric approach to modeling nonlinear relations among latent variables. Structural Equation Modeling, 12: 513–535. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar] proposed an indirect application of finite mixtures of structural equation models where latent components are estimated in the service of more flexibly recovering characteristics of the latent aggregate regression function. This article develops and evaluates delta method and parametric bootstrap approaches for obtaining approximate confidence intervals for Bauer's semiparametric approach to modeling latent nonlinear functions. Coverage rates of these approximate point-wise confidence intervals or nonsimultaneous confidence bands are evaluated by Monte Carlo and recommendations for their use are suggested.     

Monte Carlo Confidence Intervals for Complex Functions of Indirect Effects

One challenge in mediation analysis is to generate a confidence interval (CI) with high coverage and power that maintains a nominal significance level for any well-defined function of indirect and direct effects in the general context of structural equation modeling (SEM). This study discusses a proposed Monte Carlo extension that finds the CIs for any well-defined function of the coefficients of SEM such as the product of k coefficients and the ratio of the contrasts of indirect effects, using the Monte Carlo method. Finally, we conduct a small-scale simulation study to compare CIs produced by the Monte Carlo, nonparametric bootstrap, and asymptotic-delta methods. Based on our simulation study, we recommend researchers use the Monte Carlo method to test a complex function of indirect effects.     

两m相依样本均值差异的经验似然比置信区间

该文讨论了两m相依样本均值差异的经验似然的大样本性质,证明了经验似然比统计量依分布收敛于χ2随机变量,由此给出均值差异的经验似然置信区间。     

两m相依样本均值差异的经验似然比置信区间

该文讨论了两m相依样本均值差异的经验似然的大样本性质,证明了经验似然比统计量依分布收敛于x2随机变量,由此给出均值差异的经验似然置信区间.     

模拟偏差对自助法估计的影响探讨

文中探讨了模拟偏差对自助法均值估计的影响.首先,从分布N（1,12）中产生样本数据,利用自助法,得到自助法均值的估计.然后讨论了样本数据均值和总体分布均值的偏差对自助法估计的影响.结果表明,当偏差的绝对值小于等于0.54时,模拟结果较好,当偏差的绝对值大于等于0.56时,模拟结果很差.     

Bernoulli分布中参数p的近似置信区间及应用

给出了Bernoulli分布中未知参数的4种不同形式的近似置信区间,包括基于Hoeffding不等式和Bernstein不等式两种新的置信区间,并通过模拟比较了置信区间在大样本和小样本情形下的优劣.     

统计模型中误差方差的均方误差的区间估计

本文研究了线性统计模型(Ⅰ)—(Ⅳ)中参数σ^2的估计量σL^2或σH^2的均方误差MSE(σL^2)或MSE(σH^2),并分别给出了其1-α的置信区间。     

关于一个有限元误差分析的不等式

关于P1-非协调单元,我们给出从边界积分到单元积分的一个不等式中关于单元直径hK的系数C(hK)的具体值,它在相应的有限元误差分析中将起到关键作用.