广义Lorenz 曲线的非参数统计推断

本文讨论了广义Lorenz 曲线的经验似然统计推断. 在简单随机抽样、分层随机抽样和整群随机抽样下, 本文分别定义了广义Lorenz 坐标的pro le 经验似然比统计量, 得出这些经验似然比的极限分布为带系数的自由度为1 的χ² 分布. 对于整个Lorenz 曲线, 基于经验似然方法类似地得出相应的极限过程. 根据所得的经验似然理论, 本文给出了bootstrap 经验似然置信区间构造方法, 并通过数据模拟, 对新给出的广义Lorenz 坐标的bootstrap 经验似然置信区间与渐近正态置信区间以及bootstrap 置信区间等进行了对比研究. 对整个Lorenz 曲线, 基于经验似然方法对其置信域也进行了模拟研究. 最后我们将所推荐的置信区间应用到实例中.     

拟圆周的两个几何性质

§1　IntroductionLetΓbe a Jordan curve of R2 and f∶R2→R2 be a k-quasiconformal mapping,where1≤k<+∞.Γis called a quasicirlce ifΓis the image of the unit circle B2 under f.It is well-known that quasicircles play a very important role in quasiconformalmapping theory,complex dynamics,Fuchsian groups,Teichmuller space theory and lowdimensional topology,( see[1—5] etc.)In1 963 ,Ahlfors obtained the three-point property of quasidisks[6] .Later,Gehring[7] ,Osgood[8] ,Krzyz[9] ,Ch…     

关于2R（w2R）范数的一个注记

证明了自反Banach空间X上的等价w2R范数全体构成一个剩余集;同时证明了X闭子空间上等价的w2R范数均可延拓为X上等价的w2R范数.特别地,当X是可分时,上述w2R范数可替换为2R范数.     

基于模糊程度层次分析法和直觉三角模糊TOPSIS的B2R绿色供应商评价研究

针对B2R供应商评价问题,以产品竞争力、服务水平、业务能力、绿色环保能力和发展前景五个方面构建B2R供应商评价指标体系.考虑到B2R供应商评价指标的不确定性和模糊性,用模糊数来描述各指标值,基于模糊程度层次分析法(FEAHP)计算指标权重,并建立直觉三角模糊TOPSIS B2R供应商评价模型.最后,通过算例证明FEAHP和直觉三角模糊TOPSIS具有稳定性和有效性.     

DEA中连续C~2R模型理论的研究

在DEA中的C2R模型的基础上,针对决策单元输入与输出为[0,1]区间上的连续函数,建立了在一个时间区间内评价决策单元间的相对有效性的连续C2R模型以及其对偶模型,同时给出了决策单元的效率定义和弱DEA有效、DEA有效的定义.同时得到了弱对偶定理,从而初步构建了连续C2R模型的理论体系.     

SL(2,R)上Fourier变换的绝对值的渐近阶

本文研究了SL(2，R)上的Fourier变换的绝对值的渐近阶的问题．利用Lie代数SL(2，R)的表示在表示空间的作用和经典调和分析的方法，得到了SL(2，R)上的Fourier变换的绝对值的一个渐近阶．而且作为应用给出了Gc^2(2，R))上的函数的反演公式的一种新证明．     

新教材的一点启示

新教材使用后 ,笔者觉得有许多值得一提的地方 ,尤其是新增添的内容 .本文试就第一册 (下 )向量第 5.3节例题 5谈一点浅见 .1　一道例题新教材第一册 (下 )课本 P1 0 7例 5:如图 1 ,OA、OB不共线 ,AP =t AB( t∈R) ,用 OA、OB表示 OP.解　 AP =t AB,OP =OA AP =OA t AB=OA t( OB - OA)=OA t OB - t OA=( 1 - t) OA t OB.此例在教学中学生不难接受 ,但在教学时不妨告诉学生以下定理 .图 1　　　　　　　　图 22　一个定理如图 2 ,向量 a,b,c有公共起点 ,且满足c=λa μb(λ,μ∈ R) .则这三个向量…     

NA样本下基于递推型核估计的概率密度函数的经验似然推断(英文)

在NA样本下, 本文研究了基于递推型估计的概率密度函数的置信区间的构造, 证明了分块经验似然比统计量的极限分布为χ~2分布, 并利用此结果构造了概率密度函数的经验似然置信区间.     

相依样本情形时的经验似然比置信区间

本文讨论了强平稳φ混合样本的经验似然比置信区间,推广了Ｏｗｅｎ（１９８８,１９９０）在独立同分布情况下的结果,指出了相依情况时经验似然比置信区间的不足并进行了合理的改进。     

自适应逐步II型混合截尾恒加寿命试验下广义指数分布的统计分析

在自适应逐步II型混合截尾恒定应力加速寿命试验下,讨论了两参数广义指数分布的统计分析。利用EM算法和最小二乘法相结合的新方法推导出未知参数与可靠度函数的点估计,通过信息缺失原则得到了观测Fisher信息阵和尺度参数的渐近无偏估计。利用估计的渐近正态性和参数bootstrap方法构造了参数的置信区间。最后运用Monte-Carlo方法分别对得到的点估计和区间估计的精度进行研究,结果表明尺度参数的渐近无偏估计优于相应的两步估计, Boot-p置信区间比相应的渐近置信区间更精确。     

ALTERNATIVE MEASURES OF THE EXPLANATORY POWER OF GENERAL MULTIVARIATE REGRESSION MODELS

In this paper R ²-type measures of the explanatory power of multivariate linear and categorical probit models proposed in the literature are reviewed and their deficiencies discussed. It is argued that a measure of the explanatory power should take into account the components which are explicitly modelled when a regression model is estimated while it should be indifferent to components not explicitly modelled. Based on this view three different measures for multivariate probit models are proposed. Results of a simulation study are presented, designed to compare two measures in various situations, to evaluate the BC _a bootstrap technique for testing the hypothesis that the corresponding measure is zero, and to calculate approximate confidence intervals. The BC _a bootstrap technique turned out to work quite well for a wide range of situations, but may lead to misleading results if the true values of the corresponding measure are close to zero.     

Confidence Intervals and Accuracy Estimation for Heavy-Tailed Generalized Pareto Distributions

The generalized Pareto distribution (GPD) is a two-parameter family of distributions which can be used to model exceedances over a threshold. We compare the empirical coverage of some standard bootstrap and likelihood-based confidence intervals for the parameters and upper p-quantiles of the GPD. Simulation results indicate that none of the bootstrap methods give satisfactory intervals for small sample sizes. By applying a general method of D. N. Lawley, correction factors for likelihood ratio statistics of parameters and quantiles of the GPD have been calculated. Simulations show that for small sample sizes accuracy of confidence intervals can be improved by incorporating the computed correction factors to the likelihood-based confidence intervals. While the modified likelihood method has better empirical coverage probability, the mean length of produced intervals are not longer than corresponding bootstrap confidence intervals. This article also investigates the performance of some bootstrap methods for estimation of accuracy measures of maximum likelihood estimators of parameters and quantiles of the GPD.     

Comparison of Parametric and Bootstrap Approaches to Obtaining Confidence Intervals for Logspline Density Estimation

In earlier articles, we developed an automated methodology for using cubic splines with tail linear constraints to model the logarithm of a univariate density function. This methodology was subsequently modified so that the knots were determined by stepwise addition-deletion and the remaining coefficients were determined by maximum likelihood estimation. An alternative approach, referred to as the free knot spline procedure, is to use the maximum likelihood method to estimate the knot locations as well as the remaining coefficients. This article compares various approaches to constructing confidence intervals for logspline density estimates, for both the stepwise procedure and the free knot procedure. It is concluded that a variation of the bootstrap, in which only a limited number of bootstrap simulations are used to estimate standard errors that are combined with standard normal quantiles, seems to perform the best, especially when coverages and computing time are both taken into account.     

Accurate confidence intervals in regression analyses of non-normal data

A linear model in which random errors are distributed independently and identically according to an arbitrary continuous distribution is assumed. Second- and third-order accurate confidence intervals for regression parameters are constructed from Charlier differential series expansions of approximately pivotal quantities around Student’s t distribution. Simulation verifies that small sample performance of the intervals surpasses that of conventional asymptotic intervals and equals or surpasses that of bootstrap percentile-t and bootstrap percentile-|t| intervals under mild to marked departure from normality.     

Comparison on five estimation approaches of intensity for a queueing system with short run

Traffic intensity is an important measure for assessing performance of a queueing system. In this paper, we propose a consistent and asymptotically normal estimator (CAN) of intensity for a queueing system with distribution-free interarrival and service times. Using this estimator and its estimated variance, a 100(1 ? α)% asymptotic confidence interval of the intensity is constructed. Also, four bootstrap approaches—standard bootstrap, Bayesian bootstrap, percentile bootstrap, and bias-corrected and accelerated bootstrap are also applied to develop the confidence intervals of the intensity. A comparative analysis is conducted to demonstrate performances of the five confidence intervals of the intensity for a queueing system with short run data.     

Inference for the Mean Difference in the Two-Sample Random Censorship Model

Inference for the mean difference in the two-sample random censorship model is an important problem in comparative survival and reliability test studies. This paper develops an adjusted empirical likelihood inference and a martingale-based bootstrap inference for the mean difference. A nonparametric version of Wilks' theorem for the adjusted empirical likelihood is derived, and the corresponding empirical likelihood confidence interval of the mean difference is constructed. Also, it is shown that the martingale-based bootstrap gives a correct first order asymptotic approximation of the corresponding estimator of the mean difference, which ensures that the martingale-based bootstrap confidence interval has asymptotically correct coverage probability. A simulation study is conducted to compare the adjusted empirical likelihood, the martingale-based bootstrap, and Efron's bootstrap in terms of coverage accuracies and average lengths of the confidence intervals. The simulation indicates that the proposed adjusted empirical likelihood and the martingale-based bootstrap confidence procedures are comparable, and both seem to outperform Efron's bootstrap procedure.     

Computing confidence intervals for output-oriented DEA models: an application to agricultural research in Brazil

We define and model the research production at Embrapa, the major Brazilian institution responsible for applied agricultural research. The main theoretical framework is data envelopment analysis. We explore the economic interpretation and the statistical properties of these models to compute confidence intervals for output-oriented efficiency measurements. It was based on a parametric flexible model, defined by the truncated normal distribution. Intervals are calculated exploring a bootstrap approach. These results provide a better insight on the efficiency classification and allow comparisons among the decision making units involved in the evaluation process, taking into account random errors and inefficiency random variation.     

The bootstrap: Some large sample theory and connections with robustness

The bootstrap, discussed by Efron (1979, 1981), is a powerful tool for the nonparametric estimation of sampling distributions and asymptotic standard errors. We demonstrate consistency of the bootstrap distribution estimates for a general class of robust differentiable statistical functionals. Our conditions for consistency of the bootstrap are variants of previously considered criteria for robustness of the associated statistics. A general example shows that, for almost any location statistic, consistency of the bootstrap variance estimator requires a tail condition on the distribution from which samples are taken. A modification of Efron's estimator of standard error is shown to circumvent this problem.     

Unusual properties of bootstrap confidence intervals in regression problems

Summary We show that the percentile-t method, and one of the two percentile methods, have unusually good performance when employed to construct bootstrap confidence intervals in a regression setting. In the case of slope parameters, percentile-t produces two-sided intervals with coverage errorn ^-2, and one-sided intervals with coverage errorn ^-3/2, wheren is sample size. The errors are onlyn ^-1 in most other problems. One of the percentile methods produces critical points which are third-order correct for Efron's [11] relatively complex accelerated bias-corrected points.