Panel模型中的精确检验和置信区间

利用广义p-值和广义置信区间的概念,研究了Panel模型中未知参数的检验和置信区间问题.对于回归系数,分别考虑了单个情形和多个线性无关情形下的检验和置信区间问题,得到了精确检验和置信区间.对于方差分量,研究了其任意线性组合的检验和置信区间问题,建立了精确检验和置信区间.基于广义p-值和广义置信区间,获取精确检验和置信区间的方法具有计算方便、易应用于小样本问题的特点.最后,分别从理论和数值上研究了这些精确检验和置信区间的统计性质.     

线性混合模型中方差分量的广义推断

本文考虑了线性混合模型中方差分量的假设检验和区间估计问题.基于广义P-值和广义置信区间的概念,构造了对应于随机效应的单个方差分量的精确检验和置信区间.所构造的广义p-值和广义置信区间是最小充分统计量的函数.对于两个独立线性混合模型中对应于随机效应的方差分量的比较,建立了精确检验和置信区间.进-步,研究了所给检验和置信区间的统计性质,给出了这些检验方法与文献中已有方法的功效比较的模拟结果.模拟结果表明,新检验在功效方面有显著的改进.最后,通过-个实例来演示本文方怯.     

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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.     

Panel数据模型中方差分量的精确检验

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.     

Panel数据模型中方差分量的广义p值检验

利用广义p值和广义置信区间的概念构造含有四个随机效应的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.模拟结果表明,这种检验能很好地控制检验水平.     

两个Weibull分布尺度参数比的推断

本文研究两个Weibull分布尺度参数比的推断.利用广义枢轴量和广义检验变量分别给出尺度参数比的广义置信区间和假设检验.证明了在形状参数相等时由广义枢轴量确定的尺度参数比的100(1-α)%广义置信区间的覆盖概率为1-α(0＜α＜1).由广义p-值确定的固定水平检验具有真实水平.讨论了形状参数不等时尺度参数比的推断,给出频率性质,通过与前人的结果模拟比较得出本文的方法能更好地解决尺度参数比的推断问题.最后研究两个Weibull分布形状参数比的假设检验,证明由广义p-值确定的固定水平检验具有真实水平.     

偏正态非平衡面板单因素随机效应模型的Bootstrap推断

针对偏正态非平衡面板单因素随机效应模型,文章研究了回归系数和方差分量函数的假设检验和区间估计问题.首先,基于矩阵分解技术,给出回归系数的精确检验方法.其次,利用Bootstrap方法和广义方法,构造单个方差分量、方差分量之和的检验统计量和置信区间.再次,建立方差分量之比的精确检验和近似检验.文章证明了所给检验方法和置信区间的变换不变性等理论性质.Monte Carlo结果表明,对于所设参数和样本量,文章所给方法在犯第一类错误的概率和功效意义下,具有统计优良性.最后,将上述方法应用于汽油消耗量的案例分析.     

正态总体均值与标准差比在序约束下的广p-值检验

本文利用广义p-值和U-I检验法研究了多个正态总体均值与标准差比在简单半序和树序约束下的检验问题．提出了广义检验变量,得到了多个正态总体均值与标准差比在简单半序和树序约束下检验问题的广义p-值．同时运用Monte Carlo方法给出了模拟结果．     

线性混合模型方差分量的检验

对于含有两个方差分量的随机效应设计阵为任意阵的线性混合模型的方差分量单边检验问题给出了精确的F检验和基于广义p值的检验.对于给出的精确的F检验给出检验存在条件以及是一致最优无偏检验的条件.通过数值模拟,基于广义p值检验的功效和犯第一类错误的概率被讨论,由模拟结果可以看出基于广义p值的检验很好地控制了犯第一类错误的概率.     

两因素随机效应模型下平均暴露量的检验

通过两因素随机效应模型来研究某一工厂的平均暴露(exposure)水平．利用广义检验变量和广义枢轴量分别给出了相关假设检验问题的广义p-值．证明了由广义p-值所确定的拒绝域的概率在原假设下取上确界等于在原假设和备择假设的公共边界上取上确界,且进一步证明了当参数趋于原假设和备择假设的公共边界的边界时,犯第一类错误的概率趋于名义显著性水平,并在公共边界的内部做了模拟研究．结果表明,用广义p-值的方法来解决此类问题可得到令人满意的结果．     

Coverage of generalized confidence intervals

Generalized confidence intervals provide confidence intervals for complicated parametric functions in many common practical problems. They do not have exact frequentist coverage in general, but often provide coverage close to the nominal value and have the correct asymptotic coverage. However, in many applications generalized confidence intervals do not have satisfactory finite sample performance. We derive expansions of coverage probabilities of one-sided generalized confidence intervals and use the expansions to explain the nonuniform performance of the generalized intervals. We then show how to use these expansions to obtain improved coverage by suitable calibration. The benefits of the proposed modification are illustrated via several examples.     

INSTANTANEOUS AVAILABILITY ASSESSMENT OF RENEWABLE COMPONENT IN EXPONENTIAL DISTRIBUTIONS

A renewable component with exponential failure and repair times is considered, and its instantaneous availability at time t is denoted by A（t）. This paper proposes two methods for constructing lower confidence limits of A（t） with Chebyshev inequation and generalized p-value approach.     

指数分布情形下可修单元瞬时可用度评定

A renewable component with exponential failure and repair times is considered, and its instantaneous availability at time t is denoted by A(t). This paper proposes two methods for constructing lower confidence limits of A(t) with Chebyshev inequation and generalized p-value approach.     

Improved threshold diagnostic plots for extreme value analyses

A crucial aspect of threshold-based extreme value analyses is the level at which the threshold is set. For a suitably high threshold asymptotic theory suggests that threshold excesses may be modelled by a generalized Pareto distribution. A common threshold diagnostic is a plot of estimates of the generalized Pareto shape parameter over a range of thresholds. The aim is to select the lowest threshold above which the estimates are judged to be approximately constant, taking into account sampling variability summarized by pointwise confidence intervals. This approach doesn’t test directly the hypothesis that the underlying shape parameter is constant above a given threshold, but requires the user subjectively to combine information from many dependent estimates and confidence intervals. We develop tests of this hypothesis based on a multiple-threshold penultimate model that generalizes a two-threshold model proposed recently. One variant uses only the model fits from the traditional parameter stability plot. This is particularly beneficial when many datasets are analysed and enables assessment of the properties of the test on simulated data. We assess and illustrate these tests on river flow rate data and 72 series of significant wave heights.     

Inference for constant-stress accelerated degradation test based on Gamma process

This paper proposes a Gamma constant-stress accelerated degradation model based on the principle of the degradation mechanism invariance. The maximum likelihood estimators of the parameters of the proposed model are derived. Based on Cornish–Fisher expansion, the approximate confidence interval for the shape parameter of the Gamma degradation process is developed. Since it is difficult to obtain the exact confidence intervals for other model parameters and some quantities such as the mean degradation in unit time, the quantile and the reliability function of the lifetime at the normal stress level, the generalized confidence intervals for these quantities are proposed. The percentiles of the proposed generalized pivotal quantities can be obtained by the simulation. The performances of the proposed confidence intervals are evaluated by the Monte Carlo simulation method. In the simulation study, the proposed confidence intervals are compared with the Wald and the bootstrap-p confidence intervals. The simulation results show that the proposed confidence intervals outperform the Wald and the bootstrap-p confidence intervals in terms of the coverage percentage. Finally, a real example is used to illustrate the proposed procedures.     

具有随机效应的Wiener加速退化模型的可靠性研究

研究了有随机效应的Wiener退化模型基于加速退化数据的统计推断问题.利用广义枢轴量方法得到了模型参数和感兴趣可靠性指标的广义置信区间.说明了不含随机效应的Wiener退化模型的统计推断问题是有随机效应的Wiener退化模型的特殊情况.蒙特卡罗模拟结果显示文中提出的区间估计有较好的覆盖比例.最后利用LED加速退化数据说...     

Importance Sampling for p-value Computations in Multivariate Tests

Abstract

An importance sampling procedure is developed to approximate the distribution of an arbitrary function of the eigenvalues for a matrix beta random matrix or a Wishart random matrix. The procedure is easily implemented and provides confidence intervals for the p-values of many of the commonly used test statistics in multivariate analysis. An adaptive procedure allows for the control of either absolute error or relative error in this p-value estimation through the choice of importance sample size.