Best linear unbiased quantile estimators of the logistic distribution using order statistics

This paper deals with the problem of estimating the Quantiles Q(ξ), with ξ=0.01, 0.05(0.05)0.95, 0.99 of the logistic distribution by using order statistics in small samples. Linear unbiased estimators with minimum variance BLUE based on ordered observations are constructed for sample size n = 2(1)10, 15 and 20.     

A comparison of bootstrap method and Edgeworth expansion in approximating the distribution of sample variance — one sample and two sample cases

The performance of the bootstrap method and the Edgeworth expansion in approximating the distribution of sample variance are compared when the data are from a non-normal population. Both approximations are very good. so long as the parent population is close to normal.     

Approximate percentiles for ratios of f-variates

The need for percentiles of ratios of independent F-variates arises in many types of applications. Some tabulated values are available mostly for equal or nearly equal degrees-of-freedom cases, but it is not possible to provide comprehensive tables for the numerous combinations of possible degrees-of-freedom and probability levels. A simple approximation for the percentiles based on the Cornish-Fisher expansion technique is provided which is adequate for larger degrees-of-freedom and a more complicated approximation is provided which is suitable for all cases. The accuracy of the approximation is shown over a wide range of typical cases     

后“9·11”时代美国边界安全空间的外扩性趋势分析——以集装箱安全计划(CSI)为例

"9·11"后,美国边界安全政策发生了深刻变化,体现出了很多新的特点与发展趋势,边界安全空间的外扩性就是其中之一。本文拟以集装箱安全计划(CSI)为例对此进行分析,指出"9·11"后美国政府通过国际间政府合作等方式实现了美国边界安全空间的外扩,使美国的边界成为保卫边界安全的最后一道而不是第一道防线,扩大了美国边界安全保卫的战略纵深。这是"9·11"后美国政府边界安全政策的一个新特点,也是全球化时代主权国家边界安全保卫中值得探索的一种积极方式。     

Saddlepoint approximations to exact tests and improved likelihood ratio tests for the gamma distribution

For the most common one-sample and two-sample tests in the gamma distribution we derive the log likelihood ratio tests and the improved versions obtained by a Bartlett adjustment. For most of these tests an exact test exists and we give the saddlepoint approximation to the latter. The tests are compared with previously published tests and a small simulation study is included.     

Harmonic mean approach to unbalanced mixed effects models under heteroscedastic variances

In this paper we consider unbalanced mixed models (Scheffe's model) under heteroscedastic variances. By using the harmonic mean approach, It is shown that the problems appear to be anologous to those problems from balanced mixed models under homoscedastic variance. Thus, by using harmonic mean approach, statistical inferences about fixed effects and variance components are derived by using those from balanced models under homoscedastic variance. Laguerre polynomial expansion is used Lo approximate sampling distributions of relevant statistics.     

含有卷积核的线性Volterra积分微分方程的数值解

利用不动点定理证明了含有卷积核的线性Volterra积分微分方程古典解的存在性与唯一性.讨论了用TayIor公式求解该类方程的方法,并通过几个具体的例子说明这种方法的精确性.     

扩张与收缩：论美国外交的周期性

自1801年托马斯·杰斐逊总统上台以来，美国外交即呈现出“扩张——收缩——再扩张——再收缩……”的周期模式。从上一次扩张到下一次扩张或从上一次收缩到下一次收缩的平均时间约为45年左右。迄今为止，美国外交经历了四个半周期。美国经济的周期性波动、国际局势的变动、国内思潮的转换等因素是推动美国外交扩张与收缩的主要动力。当前美国外交开始步入第五个周期的收缩期，这将对世界和中国产生重大影响。     

Applications of the Bootstrap in ROC Analysis

The problem of estimating standard errors for diagnostic accuracy measures might be challenging for many complicated models. We can address such a problem by using the Bootstrap methods to blunt its technical edge with resampled empirical distributions. We consider two cases where bootstrap methods can successfully improve our knowledge of the sampling variability of the diagnostic accuracy estimators. The first application is to make inference for the area under the ROC curve resulted from a functional logistic regression model which is a sophisticated modelling device to describe the relationship between a dichotomous response and multiple covariates. We consider using this regression method to model the predictive effects of multiple independent variables on the occurrence of a disease. The accuracy measures, such as the area under the ROC curve (AUC) are developed from the functional regression. Asymptotical results for the empirical estimators are provided to facilitate inferences. The second application is to test the difference of two weighted areas under the ROC curve (WAUC) from a paired two sample study. The correlation between the two WAUC complicates the asymptotic distribution of the test statistic. We then employ the bootstrap methods to gain satisfactory inference results. Simulations and examples are supplied in this article to confirm the merits of the bootstrap methods.     

Comparison of powers for the sphericity tests using both the asymptotic distribution and the bootstrap

The asymptotic distributions of two tests for sphericity:the locally most powerful invariant test and the likelihood ratio test are derived under the general alternaties ∑?σ² I. The powers of these two tests are then compared when the data are from a trivariate normal population. The bootstrap method is also used to obtain the powers and the powers obtained by this method agree with those from the asymptotic distributions.