Nonparametric control charts based on runs and Wilcoxon-type rank-sum statistics

In this article, we introduce three new distribution-free Shewhart-type control charts that exploit run and Wilcoxon-type rank-sum statistics to detect possible shifts of a monitored process. Exact formulae for the alarm rate, the run length distribution, and the average run length (ARL) are all derived. A key advantage of these charts is that, due to their nonparametric nature, the false alarm rate (FAR) and in-control run length distribution is the same for all continuous process distributions. Tables are provided for the implementation of the charts for some typical FAR values. Furthermore, a numerical study carried out reveals that the new charts are quite flexible and efficient in detecting shifts to Lehmann-type out-of-control situations.     

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.     

长三角科技资源配置能力与城市化进程的协调耦合关系研究

科技资源配置能力已成为长江地区城市化进程的重要推力。因此,在构建科技资源与城市化耦合系统评价指标体系的基础上,利用耦合协调度模型综合评价长江区域科技资源配置与城市化的交互耦合关系。结果显示:从时间维度看,研究期内长三角科技资源配置能力与城市化进程之间的耦合关系基本上处于磨合阶段,耦合协调度以低度协调耦合状态为主并逐步过渡到中度协调耦合状态;从空间维度看,长三角各城市的科技资源配置与城市化耦合协调度在极度协调耦合、高度协调耦合、中度协调耦合、低度协调耦合四个阶段均有分布,层级分明且大部分城市尚处于低度协调耦合状态。     

基于灰色关联的西部煤炭产业集中度影响因素研究

在概述西部原煤产量及其矿井类型与数量变化趋势的基础上,利用2003-2010年相关时序数据测度了西部煤炭产业在这一时期的集中度。随后,运用灰色关联理论,分析了期初集中度、生产扩张能力、进入壁垒、市场容量等相关因素与西部煤炭产业集中度的灰色关联程度。研究表明:期初集中度与市场容量是影响西部煤炭产业集中度诸多因素中最为重要的两个因素。在进一步分析产生这一结果深层原因的基础上,提出了提高西部煤炭产业集中度的政策建议。     

Darling–Erdős limit results for change-point detection in panel data

We wish to test the null hypothesis if the means of N panels remain the same during the observation period of length T. A quasi-likelihood argument leads to self-normalized statistics whose limit distribution under the null hypothesis is double exponential. The main results are derived assuming that the each panel is based on independent observations and then extended to linear processes. The proofs are based on an approximation of the sum of squared CUSUM processes using the Skorokhod embedding scheme. A simulation study illustrates that our results can be used in case of small and moderate N and T. We apply our results to detect change in the “corruption index”.     

On the use of curve fitting to model the error of the Cornish-Fisher expansion of the pearson type-VI distribution

The Cornish-Fisher expansion of the Pearson type VI distribution is known to be reasonably accurate when both degrees of freedom are relatively large (say greater than or equal to 5). However, when either or both degrees of freedom are less than 5, the accuracy of the computed percentage point begins to suffer; in some cases severely. To correct for this, the error surface in the degrees of freedom plane is modeled by least squares curve fitting for selected levels of tail probability (.025, .05, and .10) which can be used to adjust the percentage point obtained from the usual Cornish-Fisher expansion. This adjustment procedure produces a computing algorithm that computes percentage points of the Pearson type VI distribution at the above probability levels, accurate to at least + 1 in 3 digits in approximately 11 milliseconds per subroutine call on an IBM 370/145. This adjusted routine is valid for both degrees of freedom greater than or equal to 1.     

Tests of hypotheses based on ranks in the general linear model

A unified approach is developed for testing hypotheses in the general linear model based on the ranks of the residuals. It complements the nonparametric estimation procedures recently reported in the literature. The testing and estimation procedures together provide a robust alternative to least squares. The methods are similar in spirit to least squares so that results are simple to interpret. Hypotheses concerning a subset of specified parameters can be tested, while the remaining parameters are treated as nuisance parameters. Asymptotically, the test statistic is shown to have a chi-square distribution under the null hypothesis. This result is then extended to cover a sequence of contiguous alternatives from which the Pitman efficacy is derived. The general application of the test requires the consistent estimation of a functional of the underlying distribution and one such estimate is furnished.     

A Nonstochastic Interpretation of Reported Significance Levels

Tests of significance are often made in situations where the standard assumptions underlying the probability calculations do not hold. As a result, the reported significance levels become difficult to interpret. This article sketches an alternative interpretation of a reported significance level, valid in considerable generality. This level locates the given data set within the spectrum of other data sets derived from the given one by an appropriate class of transformations. If the null hypothesis being tested holds, the derived data sets should be equivalent to the original one. Thus, a small reported significance level indicates an unusual data set. This development parallels that of randomization tests, but there is a crucial technical difference: our approach involves permuting observed residuals; the classical randomization approach involves permuting unobservable, or perhaps nonexistent, stochastic disturbance terms.     

Simulation of the p-generalized Gaussian distribution

In this paper, we introduce the p-generalized polar methods for the simulation of the p-generalized Gaussian distribution. On the basis of geometric measure representations, the well-known Box–Muller method and the Marsaglia–Bray rejecting polar method for the simulation of the Gaussian distribution are generalized to simulate the p-generalized Gaussian distribution, which fits much more flexibly to data than the Gaussian distribution and has already been applied in various fields of modern sciences. To prove the correctness of the p-generalized polar methods, we give stochastic representations, and to demonstrate their adequacy, we perform a comparison of six simulation techniques w.r.t. the goodness of fit and the complexity. The competing methods include adapted general methods and another special method. Furthermore, we prove stochastic representations for all the adapted methods.