Generalized Sobol sensitivity indices for dependent variables: numerical methods

The hierarchically orthogonal functional decomposition of any measurable function η of a random vector X=(X₁,?…?, X_p) consists in decomposing η(X) into a sum of increasing dimension functions depending only on a subvector of X. Even when X₁,?…?, X_p are assumed to be dependent, this decomposition is unique if the components are hierarchically orthogonal. That is, two of the components are orthogonal whenever all the variables involved in one of the summands are a subset of the variables involved in the other. Setting Y=η(X), this decomposition leads to the definition of generalized sensitivity indices able to quantify the uncertainty of Y due to each dependent input in X [Chastaing G, Gamboa F, Prieur C. Generalized Hoeffding–Sobol decomposition for dependent variables – application to sensitivity analysis. Electron J Statist. 2012;6:2420–2448]. In this paper, a numerical method is developed to identify the component functions of the decomposition using the hierarchical orthogonality property. Furthermore, the asymptotic properties of the components estimation is studied, as well as the numerical estimation of the generalized sensitivity indices of a toy model. Lastly, the method is applied to a model arising from a real-world problem.     

Variable selection in partial linear regression with functional covariate

The problem of variable selection is considered in high-dimensional partial linear regression under some model allowing for possibly functional variable. The procedure studied is that of nonconcave-penalized least squares. It is shown the existence of a √n/s_n-consistent estimator for the vector of p_n linear parameters in the model, even when p_n tends to ∞ as the sample size n increases (s_n denotes the number of influential variables). An oracle property is also obtained for the variable selection method, and the nonparametric rate of convergence is stated for the estimator of the nonlinear functional component of the model. Finally, a simulation study illustrates the finite sample size performance of our procedure.     

Measures of Association and Visualization of Log Odds Ratio Structure for a Two Way Contingency Table

The odds ratio (OR) is a measure of association used for analysing an I × J contingency table. The total number of ORs to check grows with I and J. Several statistical methods have been developed for summarising them. These methods begin from two different starting points, the I × J contingency table and the two‐way table composed by the ORs. In this paper we focus our attention on the relationship between these methods and point out that, for an exhaustive analysis of association through log ORs, it is necessary to consider all the outcomes of these methods. We also introduce some new methodological and graphical features. In order to illustrate previously used methodologies, we consider a data table of the cross‐classification of the colour of eyes and hair of 5387 children from Scotland. We point out how, through the log OR analysis, it is possible to extract useful information about the association between variables.     

关于向量空间的准素分解

本文讨论了向量空间关于线性变换σ的准素分解的一些推广形式。     

上海与纽约黄金期货价格联动关系实证分析

为研究国内外期货黄金价格之间的关联性,对2011～ 2012年间的纽约期金日收盘价格和上海期金开盘价格进行协整检验、因果检验,建立误差修正模型,进行脉冲响应分析和方差分解研究.结果表明：上海黄金期货市场与纽约黄金期货市场价格之间存在长期均衡的关系.上海期货价格受到纽约期货市场价格的影响幅度更大,时间间隔更短.     

基于VAR模型的安徽省粮食产量影响因素的实证研究

自然条件、政策环境、经济因素、技术进步等因素都会影响粮食产量。选取安徽省1990-2012年影响粮食生产的7个因素,最初,使用前向逐步回归分析的方法研究发现,对粮食产量影响较大的因素有粮食成灾面积、有效灌溉面积、化肥施用量3个变量。其次,Johansen协整检验阐释了这3个变量与粮食总产量之间的关系,并构造脉冲响应函数及进行方差分解得出这3个变量对总产量的贡献度为：粮食成灾面积〉化肥施用量〉有效灌溉面积。所以,增强农业工程的防灾减灾效果,提升农田水利基础设施的使用效率,科学控制化肥施用量对提高安徽省粮食综合生产能力具有重大作用。     

国际干散货运输航线间即期与远期市场的关联机制研究

以C3、C5航线FFA交易即期和远期的日数据为研究对象,以向量自回归模型为基础,利用脉冲响应分析和方差分解分析方法,对C3、C5航线的即期与远期市场及其航线间的相关关系进行了实证分析。脉冲响应结果显示,同一航线即期市场的波动会引起远期市场的波动,反之则影响较小;C5航线的波动能迅速传给C3航线,反之则较弱。通过方差分解分析可以发现,即期市场的预测波动大约有50％来源于对应的远期市场但远期市场的预测波动主要取决于远期市场本身;C3航线的预测波动主要取决于本航线,而C5航线的预测波动则有一半来源于C3航线。     

基于光电传感器的目标轮廓提取及其识别

针对物体外形轮廓特征,给出一种基于主动式光电传感器的轮廓特征提取方法,该方法是通过物体经过传感器组视场时各传感器输出状态来获取特征信息;并结合稀疏表示理论,提出一种基于稀疏表示的目标轮廓识别算法,该算法是将测试样本投影到稀疏域,依据系数的稀疏性对测试样本进行分类。数值仿真与实验结果表明：采用光电传感器组获取的信息能够有效地描述物体;且通过本文算法对不同类型物体进行分类,具有良好的识别效果;对不同条件下获得的特征样本进行分类时,具有良好的鲁棒性。     

A simple way to obtain the spectral decomposition of variance components models for balanced data

By means of an example it is shown how eigenvalues and eigenvectors of variance components models can be obtained straightforwardly when balanced data are available. Simple asymptotically efficient estimators of the variance components are presented.