Some Q-Q Probability Plots to Test Spherical and Elliptical Symmetry

Abstract

This article proposes some probability plots are proposed to test spherical and elliptical symmetry in terms of some invariant statistics under orthogonal transformations. Some correlation coefficients as numerical measures of detecting deviation from spherical or elliptical symmetry are recommended, and the empirical percentiles of these correlation coefficients are calculated by simulation. The simulation results for data sets from 12 different populations show that the new plots are useful for testing spherical and elliptical symmetry. Some discussion is given also.     

Residual Diagnostics for Covariate Effects in Spatial Point Process Models

For a spatial point process model in which the intensity depends on spatial covariates, we develop graphical diagnostics for validating the covariate effect term in the model, and for assessing whether another covariate should be added to the model. The diagnostics are point-process counterparts of the well-known partial residual plots (component-plus-residual plots) and added variable plots for generalized linear models. The new diagnostics can be derived as limits of these classical techniques under increasingly fine discretization, which leads to efficient numerical approximations. The diagnostics can also be recognized as integrals of the point process residuals, enabling us to prove asymptotic results. The diagnostics perform correctly in a simulation experiment. We demonstrate their utility in an application to geological exploration, in which a point pattern of gold deposits is modeled as a point process with intensity depending on the distance to the nearest geological fault. Online supplementary materials include technical proofs, computer code, and results of a simulation study.     

Hierarchical Model-Based Clustering for Large Datasets

In recent years, hierarchical model-based clustering has provided promising results in a variety of applications. However, its use with large datasets has been hindered by a time and memory complexity that are at least quadratic in the number of observations. To overcome this difficulty, this article proposes to start the hierarchical agglomeration from an efficient classification of the data in many classes rather than from the usual set of singleton clusters. This initial partition is derived from a subgraph of the minimum spanning tree associated with the data. To this end, we develop graphical tools that assess the presence of clusters in the data and uncover observations difficult to classify. We use this approach to analyze two large, real datasets: a multiband MRI image of the human brain and data on global precipitation climatology. We use the real datasets to discuss ways of integrating the spatial information in the clustering analysis. We focus on two-stage methods, in which a second stage of processing using established methods is applied to the output from the algorithm presented in this article, viewed as a first stage.     

HE Plots for Multivariate Linear Models

Multivariate analysis of variance (MANOVA) extends the ideas and methods of univariate ANOVA in simple and straightforward ways. But the familiar graphical methods typically used for univariate ANOVA are inadequate for showing how measures in a multivariate response vary with each other, and how their means vary with explanatory factors. Similarly, the graphical methods commonly used in multiple regression are not widely available or used in multivariate multiple regression (MMRA). We describe a variety of graphical methods for multiple-response (MANOVA and MMRA) data aimed at understanding what is being tested in a multivariate test, and how factor/predictor effects are expressed across multiple response measures.

In particular, we describe and illustrate: (a) Data ellipses and biplots for multivariate data; (b) HE plots, showing the hypothesis and error covariance matrices for a given pair of responses, and a given effect; (c) HE plot matrices, showing all pairwise HE plots; and (d) reduced-rank analogs of HE plots, showing all observations, group means, and their relations to the response variables. All of these methods are implemented in a collection of easily used SAS macro programs.     

基于POT方法的商业银行操作风险极端值估计

对于商业银行而言,操作风险已经成为与市场风险和信用风险同样重要的风险。本文利用极值理论超越样本的估计能力,采用极值理论中对数据要求量较少,可以进行单步预测的超阈值(POT)方法对我国商业银行操作损失极端值分布进行估计,以均值超额函数图和拟合直线的交点确定阈值,估计出给定置信水平之下操作风险损失的分位数,从而使得国内商业银行操作风险监管资本的计算成为可能。     

Empirical process approach to some two-sample problems based on ranked set samples

We study the asymptotic properties of both the horizontal and vertical shift functions based on independent ranked set samples drawn from continuous distributions. Several tests derived from these shift processes are developed. We show that by using balanced ranked set samples with bigger set sizes, one can decrease the width of the confidence band and hence increase the power of these tests. These theoretical findings are validated through small-scale simulation studies. An application of the proposed techniques to a cancer mortality data set is also provided. Part of the research was conducted while Kaushik Ghosh was visiting Statistical Research and Applications Branch of the National Cancer Institute on an Intergovernmental Personnel Assignment.     

Effect of substrate temperature on structural, optical and electrical properties of pulsed laser ablated nanostructured indium oxide films

Nanocrystalline indium oxide (INO) films are deposited in a back ground oxygen pressure at 0.02 mbar on quartz substrates at different substrate temperatures (T_s) ranging from 300 to 573 K using pulsed laser deposition technique. The films are characterized using GIXRD, XPS, AFM and UV-visible spectroscopy to study the effect of substrate temperature on the structural and optical properties of films. The XRD patterns suggest that the films deposited at room temperature are amorphous in nature and the crystalline nature of the films increases with increase in substrate temperature. Films prepared at T_s ≥ 473 K are polycrystalline in nature (cubic phase). Crystalline grain size calculation based on Debye Scherrer formula indicates that the particle size enhances with the increase in substrate temperature. Lattice constant of the films are calculated from the XRD data. XPS studies suggest that all the INO films consist of both crystalline and amorphous phases. XPS results show an increase in oxygen content with increase in substrate temperature and reveals that the films deposited at higher substrate temperatures exhibit better stoichiometry. The thickness measurements using interferometric techniques show that the film thickness decreases with increase in substrate temperature. Analysis of the optical transmittance data of the films shows a blue shift in the values of optical band gap energy for the films compared to that of the bulk material owing to the quantum confinement effect due to the presence of quantum dots in the films. Refractive index and porosity of the films are also investigated. Room temperature DC electrical measurements shows that the INO films investigated are having relatively high electrical resistivity in the range of 0.80-1.90 Ωm. Low temperature electrical conductivity measurements in the temperature range of 50-300 K for the film deposited at 300 K give a linear Arrhenius plot suggesting thermally activated conduction. Surface morphology studies of the films using AFM reveal the formation of nanostructured indium oxide thin films.     

人工湿地技术削减雨水初期径流污染负荷研究进展

拟从技术特点、技术流程、技术原理、技术参数、技术使用中存在的问题以及技术的应用前景等方面对雨水初期径流污染人工湿地技术进行分析和描述.介绍了该技术在国内和国外的研究现状,并展望了其未来研究方向.以期为我国城市雨水初期径流污染控制工程提供参考依据.     

龙羊峡电站下闸蓄水水情长期预报的神经网络方法研究

误差反向传播算法(BP算法)是训练多层网络的常用算法,但难于确定网络的有效隐节点数,本文提出了一个有效的算法来自动优选隐层节点数,文中用龙羊峡水电站历年10月份的系列实测资料进行了实例研究,取得了初步令人满意的结果。     

福建省水循环要素分析

本文从环境水文学的观点出发,应用水量平衡理论对福建省的水循环进行探讨。分析了福建省水汽输送,降水、蒸发及径流的特性,它们的地理分布和年际变化规律。阐明了水循环诸要素之间的关系以及人类活动对水循环的影响,并对水量供需平衡进行分析。