NONPARAMETRIC TWO SAMPLE TESTS BASED ON AREA STATISTICS

ABSTRACT

Area statistics are sample versions of areas occurring in a probability plot of two distribution functions F and G. This paper presents a unified basis for five statistics of this type. They can be used for various testing problems in the framework of the two sample problem for independent observations, such as testing equality of distributions against inequality or testing stochastic dominance of distributions in one or either direction against nondominance. Though three of the statistics considered have already been suggested in literature, two of them are new and deserve our interest. The finite sample distributions of the statistics (under F=G) can be calculated via recursion formulae. Two tables with critical values of the new statistics are included. The asymptotic distribution of the properly normalized versions of the area statistics are functionals of the Brownian bridge. The distribution functions and quantiles thereof are obtained by Monte Carlo simulation. Finally, the power functions of the two new tests based on area statistics are compared to the power functions of the tests based on the corresponding supremum statistics, i.e., statistics of the Kolmogorov–Smirnov type.     

Estimation of a process capability index for inverse gaussian distribution

In this article, interval estimates of Clements' process capability index are studied through bootstrapping when the underlying distribution is Inverse Gaussian. The standard bootstrap, the percentile bootstrap, and the bias-corrected percentile bootstrap confidence intervals are compared.     

大都市的扩展历程与大都市边缘区的城乡一体化问题分析

以一座三塔悬索桥为分析对象,采用SAP2000平台建立该桥空间动力有限元模型并进行非线性动力分析,研究了地震作用下,缆梁间设置中央扣、中塔与主梁间设置弹性索和二者组合使用对于该桥抗震性能的影响。分析结果表明,缆梁间设置中央扣可以显著减小主梁位移和中塔塔底剪力和弯矩,但会使各塔顶主索鞍座水平力和边塔内力增加;选用合理的弹性索刚度,可以有效控制主梁位移,同时使中塔与边塔的受力处于合理范围内;两者组合使用,能够进一步降低主梁位移和均衡中塔与边塔的受力,同时可以减小弹性索索力,更有利于中塔下横梁受力。     

基于模糊理论评估连续梁桥地震破坏状况

为了研究不同强度等级地震作用下连续梁桥的破坏模式及破坏程度,采用多级模糊综合评判方法建立连续梁桥的综合评估模型。根据连续梁桥的特点,利用连续梁桥各单元及各构件的破坏程度建立多个因素集,根据各因素的权重和评价标准,对多个因素集进行逐级评判,根据最大隶属度原则得到地震作用下连续梁桥的破坏情况,并通过等级参数评判法对不同地震强度下连续梁桥的破坏情况进行等级评判,得到连续梁桥破坏情况与地震强度之间的关系。最后,基于多级模糊综合评判方法对一座连续梁桥实例进行评判     

桥塞坐封过程仿真模拟研究

桥塞作为井下封层技术的关键设备,由于它施工工序少、周期短、卡封位置准确而得到了广泛应用。针对设计的可钻式非金属桥塞坐封过程开展模拟研究,涉及弹塑性材料接触、超弹性材料接触和非金属材料动态断裂的非线性动力学问题,利用有限元法建立该桥塞全尺寸模型和所有部件之间的广义接触关系,通过有限元模拟动态坐封过程获得桥塞各部件运动变形特性、桥塞与套管之间的密封特性和动态坐封力等数据,该桥塞坐封完成时,坐封机构部件轴向位移110 mm,坐封力约45 kN。模拟坐封也为进一步优化该型桥塞的结构和评估坐封性能提供了理论依据,对该型桥塞的推广应用奠定了基础。     

A Necessary Condition for the Strong Oracle Property

A problem of using a non‐convex penalty for sparse regression is that there are multiple local minima of the penalized sum of squared residuals, and it is not known which one is a good estimator. The aim of this paper is to give a guide to design a non‐convex penalty that has the strong oracle property. Here, the strong oracle property means that the oracle estimator is the unique local minimum of the objective function. We summarize three definitions of the oracle property – the global, weak and strong oracle properties. Then, we give sufficient conditions for the weak oracle property, which means that the oracle estimator becomes a local minimum. We give an example of non‐convex penalties that possess the weak oracle property but not the strong oracle property. Finally, we give a necessary condition for the strong oracle property.     

道路与桥梁专业校企合作共建实践教学基地模式探析

高职院校应培养有较强实践能力的实用型人才。然而,我国高职院校专业教学中的理论教学与实践教学往往难以融为一体,培养出的学生很难达到企业的要求。校企合作共建实践教学基地,是破解此弊端的一剂良方。文章就江西交通职业技术学院校企合作共建实践教学基地做了探析。     

Nonparametric and semiparametric estimation of the three way receiver operating characteristic surface

In many situations the diagnostic decision is not limited to a binary choice. Binary statistical tools such as receiver operating characteristic (ROC) curve and area under the ROC curve (AUC) need to be expanded to address three-category classification problem. Previous authors have suggest various ways to model the extension of AUC but not the ROC surface. Only simple parametric approaches are proposed for modeling the ROC measure under the assumption that test results all follow normal distributions. We study the estimation methods of three-dimensional ROC surfaces with nonparametric and semiparametric estimators. Asymptotical results are provided as a basis for statistical inference. Simulation studies are performed to assess the validity of our proposed methods in finite samples. We consider an Alzheimer's disease example from a clinical study in the US as an illustration. The nonparametric and semiparametric modelling approaches for the three way ROC analysis can be readily generalized to diagnostic problems with more than three classes.     

Multivariate log-Birnbaum–Saunders regression models

In this paper, we present a multivariate version of the skewed log-Birnbaum–Saunders regression model. This new family of distributions holds good properties such as marginal variables following univariate skewed log-Birnbaum–Saunders distributions, besides presenting the usual log-Birnbaum–Saunders distribution as a particular case. Furthermore, the model parameters are estimated through maximum-likelihood methods, a closed-form expression for the Fisher’s information matrix is presented, and testing hypothesis for model parameters is performed. Two real datasets are analyzed and results are discussed.