概化理论方差分量置信区间估计Bootstrap方法比较

使用Monte Carlo模拟技术生成多项分布数据,比较四种Bootstrap方法估计概化理论方差分量置信区间的性能,四种Bootstrap方法分别是Bootstrap-PC、Bootstrap-t、Bootstrap-BCa和Bootstrap-ABC方法.结果表明:(1)从整体上看,四种Bootstrap方法估计方差分量置信区间的包含率,校正的Bootstrap方法要优于未校正的Bootstrap方法;(2)校正的Bootstrap-PC和Bootstrap-t方法相当,校正的Bootstrap-BCa与Bootstrap-ABC方法相当,校正的Bootstrap-BCa和Bootstrap-ABC方法要优于校正的Bootstrap-PC和Bootstrap-t方法.     

平均处理效果估计的Bootstrap置信区间确定方法

人们越来越关注经济现象中平均处理效果的估计.但在实际操作中,进行平均处理效果的无偏估计是比较困难的.因此引入了倾向度并通过最大似然估计的方法求出了倾向度的估计值,从而得出平均处理效果的数学期望.文章对协变量服从二点分布和多项分布的情形,讨论了它的平均处理效果估计并给出了其Bootstrap置信区间.     

非正态过程能力指数估计与Bootstrap置信区间构建

传统计算非正态分布过程能力指数最经典的方法——Clement方法,其最大的缺点是必须有足够多的观测样本才能得到较为准确的结果。文章利用加权标准差可将非正态过程分解成两个正态过程的思想,结合样本估计相关理论构建了一种基于加权标准差的过程能力指数。新指数无论是在小样本还是大样本的情况下,都比Clement方法估计结果的准确性更高,且在此方法基础上构建的Bootstrap置信区间的真实值覆盖率均远远高于同等条件下Clement方法构建的置信区间。     

泊松分布变异系数的贝叶斯估计

文章在熵损失函数下,针对一组泊松样本,用参数估计方法研究了泊松分布变异系数的贝叶斯估计问题,得到了变异系数的贝叶斯估计的一般形式与精确形式,并讨论了它的可容许性。最后在给定置信水平1-α下研究了变异系数的贝叶斯置信区间。模拟结果表明这两种估计都具有较高的精度。     

Behrens-Fisher问题的广义置信区间

文章给出了Behrens-Fisher问题的广义置信区间及其计算方法,通过模拟研究验证了方法的可行性,并与Welch&Aspin近似及Bayes精确区间估计方法进行了比较,结果显示广义置信区间方法有更高的精度。     

相关数据下比率置信区间构造方法的改进

一类相关数据在医学诊断等应用领域普遍存在,这种数据下来自同一个体的多个观察存在相关.对于二分类相关数据比率置信区间的构造,文章引用二项分布Agresti-Coull区间的构造思想,在已有的Donner-Klar区间上基于调整midpoint和缩小方差估计量改进得到一种新的置信区间.通过蒙特卡洛数值模拟,结果表明改进区间比目前常用的三种区间不仅有更好的区间覆盖率,而且区间宽度较小.     

二项分布下基于鞍点逼近的总体成数置信区间的构造

面对总体成数置信区间的估计问题,可以采用二项分布下基于鞍点逼近的方法来构造总体成数的置信区间,这种方法为总体成数的区间估计提供了一种新的途径,将其和传统的区间估计方法比较,即正态近似法和枢轴量法进行比较。蒙特卡洛模拟和实例分析的结果为:在几种不同的置信区间构造方法中,小样本情况下,鞍点逼近方法构造的总体成数的置信区间长度相对较短,覆盖率最接近名义水平;大样本下,鞍点逼近方法整体表现最优。因此,可以得到鞍点逼近法对总体成数置信区间的估计较为精确,尤其是小样本情况下更为适用的结论。     

含均值结构变点时间序列的贝叶斯单位根检验

针对ADF和PP检验对含有均值结构变点时间序列的“伪检验”问题,文章基于贝叶斯理论,先运用贝叶斯因子模型选择的方法检测时序结构变点位置,再在结构变点已知的情况下运用置信区间和贝叶斯因子两种方法检验序列是否存在单位根,并用Monte Carlo模拟方法进行仿真,验证该方法的有效性。研究发现：是否考虑均值结构变点对时间序列的单位根检验有着重要的影响,不考虑结构突变而进行常规的单位根检验会产生误判;贝叶斯方法能够有效检测含有均值结构变点时间序列的变点位置,并能提高单位根检验功效。     

近单位根过程脉冲响应函数的置信区间

本文提出一个构造近单位根自回归过程脉冲响应函数的置信区间的新方法。新方法首先修正自回归系数估计的偏误,然后利用标准自举方法构造脉冲响应函数的置信区间。蒙特卡罗模拟结果表明在小样本时新方法的表现要明显优于已有的方法。新方法的实际覆盖率能够一致地达到或超过名义置信水平。     

关于捕获再捕获抽样的置信区间

捕获再捕获抽样是一种应用广泛的抽样方法。运用随机模拟,研究捕获再捕获抽样的三种估计量的均值、方差、偏度、峰度、利用近似正态分布构造的置信区间的统计性质。改进了估计量的样本方差计算公式,使得利用近似正态分布构造的置信区间更优。     

Percentile-t Bootstrap Confidence Intervals for Period Using Periodogram

The magnitude of light intensity of many stars varies over time in a periodic way. Therefore, estimation of period and making inference about this parameter are of great interest in astronomy. The periodogram can be used to estimate period, properly. Bootstrap confidence intervals for period suggested here, are based on using the periodogram and constructed by percentile-t methods. We prove that the equal-tailed percentile-t bootstrap confidence intervals for period have an error of order n ^?1. We also show that the symmetric percentile-t bootstrap confidence intervals reduce the error to order n ^?2, and hence have a better performance. Finally, we assess the theoretical results by conducting a simulation study, compare the results with the coverages of percentile bootstrap confidence intervals for period and then analyze a real data set related to the eclipsing system R Canis Majoris collected by Shiraz Biruni Observatory.     

Balanced Confidence Regions Based on Tukey's Depth and the Bootstrap

We propose and study the bootstrap confidence regions for multivariate parameters based on Tukey's depth. The bootstrap is based on the normalized or Studentized statistic formed from an independent and identically distributed random sample obtained from some unknown distribution in R ^q . The bootstrap points are deleted on the basis of Tukey's depth until the desired confidence level is reached. The proposed confidence regions are shown to be second order balanced in the context discussed by Beran. We also study the asymptotic consistency of Tukey's depth-based bootstrap confidence regions. The applicability of the method proposed is demonstrated in a simulation study.     

Median Control Charts Based on Bootstrap Method

In this study, we propose a median control chart. In order to determine the control limits, we consider using an estimate of the variance of sample median. Also, we consider applying the bootstrap methods. Then we illustrate the proposed median control chart with an example and compare the bootstrap methods by simulation study. Finally, we discuss some peculiar features for the median control chart as concluding remarks.     

A Smooth Bootstrap Procedure towards Deriving Confidence Intervals for the Relative Risk

Given a pair of sample estimators of two independent proportions, bootstrap methods are a common strategy towards deriving the associated confidence interval for the relative risk. We develop a new smooth bootstrap procedure, which generates pseudo-samples from a continuous quantile function. Under a variety of settings, our simulation studies show that our method possesses a better or equal performance in comparison with asymptotic theory based and existing bootstrap methods, particularly for heavily unbalanced data in terms of coverage probability and power. We illustrate our procedure as applied to several published data sets.     

On Properties of Percentile Bootstrap Confidence Intervals for Period Using Periodogram

Periodic functions have many applications in astronomy. They can be used to model the magnitude of light intensity of the period variable stars that their brightness vary with time. Because the data related to the astronomical applications are commonly observed at the time points that are not regularly spaced, the use of the periodogram as a good tool for estimating period is highlighted. Our bootstrap inference about period is based on maximizing the periodogram and consists of percentile two-sided bootstrap confidence intervals construction for the true period. We also obtain their coverage levels theoretically, and discuss the benefit of double-bootstrap confidence intervals for the parameter by which the coverage levels are substantially improved. Precisely, we show that the coverage error of single-bootstrap confidence intervals is of order n ^?1, decreasing to order n ^?2 when applying double-bootstrap methods. The simulation study given here is a numerical assessment of the theoretical work.     

Nonparametric Interval Estimation in One-Way Random-Effects Models

The structural method provided by Hannig et al. (2006 Hannig , J. , Iyer , H. , Patterson , P. (2006). Fiducial generalized confidence intervals. J. Amer. Statist. Assoc. 101:254–269.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) has proved to be a useful tool for constructing confidence intervals. However, it is difficult to apply this method to nonparametric problems since the pivotal quantity required in using it exists only in some special parametric models. Based on an extended structural method, this article discusses nonparametric interval estimation for smooth functions of the variances in one-way random-effects models. We use the bootstrap distribution estimator of a statistic to construct an approximate pivotal equation, and prove that the confidence interval derived by the approximate pivotal equation has asymptotically correct coverage probability. Simulation results are presented and show that the normal fiducial interval is not robust against non normality and that the proposed confidence interval has better finite-sample behaviors than the naive interval based on normal approximation.     

Sequential Fixed-Width Confidence Interval for a Function of the Parameters

Let X₁…, X_m and Y₁…, Y_n be two independent sequences of i.i.d. random variables with distribution functions F_x(.|θ) and F_y(. | φ) respectively. Let g(θ, φ) be a real-valued function of the unknown parameters θ and φ. The purpose of this paper is to suggest a sequential procedure which gives a fixed-width confidence interval for g(θ, φ) so that the coverage probability is approximately α (preas-signed). Certain asymptotic optimality properties of the sequential procedure are established. A Monte Carlo study is presented.     

Kernel Smoothing to Improve Bootstrap Confidence Intervals

Some studies of the bootstrap have assessed the effect of smoothing the estimated distribution that is resampled, a process usually known as the smoothed bootstrap. Generally, the smoothed distribution for resampling is a kernel estimate and is often rescaled to retain certain characteristics of the empirical distribution. Typically the effect of such smoothing has been measured in terms of the mean-squared error of bootstrap point estimates. The reports of these previous investigations have not been encouraging about the efficacy of smoothing. In this paper the effect of resampling a kernel-smoothed distribution is evaluated through expansions for the coverage of bootstrap percentile confidence intervals. It is shown that, under the smooth function model, proper bandwidth selection can accomplish a first-order correction for the one-sided percentile method. With the objective of reducing the coverage error the appropriate bandwidth for one-sided intervals converges at a rate of n ^−1/4, rather than the familiar n ^−1/5 for kernel density estimation. Applications of this same approach to bootstrap t and two-sided intervals yield optimal bandwidths of order n ^−1/2. These bandwidths depend on moments of the smooth function model and not on derivatives of the underlying density of the data. The relationship of this smoothing method to both the accelerated bias correction and the bootstrap t methods provides some insight into the connections between three quite distinct approximate confidence intervals.     

A Stepwise Confidence Interval Procedure Under Unknown Variances Based on an Asymmetric Loss Function for Toxicological Evaluation

One of the most important issues in toxicity studies is the identification of the equivalence of treatments with a placebo. Because it is unacceptable to declare non‐equivalent treatments to be equivalent, it is important to adopt a reliable statistical method to properly control the family‐wise error rate (FWER). In dealing with this issue, it is important to keep in mind that overestimating toxicity equivalence is a more serious error than underestimating toxicity equivalence. Consequently asymmetric loss functions are more appropriate than symmetric loss functions. Recently Tao, Tang & Shi (2010) developed a new procedure based on an asymmetric loss function. However, their procedure is somewhat unsatisfactory because it assumes that the variances of various dose levels are known. This assumption is restrictive for some applications. In this study we propose an improved approach based on asymmetric confidence intervals without the restrictive assumption of known variances. The asymmetry guarantees reliability in the sense that the FWER is well controlled. Although our procedure is developed assuming that the variances of various dose levels are unknown but equal, simulation studies show that our procedure still performs quite well when the variances are unequal.