Research on Some Questions About Selection of Independent Variables

1　 IntroductionMultivariate is one of the most widely used branches of Statistics.The major uses are asfollows:1It is used to describe and explain phenomenon,when we expect the number ofindependent variables included in a regression equation to be reduced to the utmost.2 Itisused in prediction,when we expect MSE of prediction to be rather small.3 Itis used incontrol,when we expect the variance and MSE of each regression parameter to be rathersmall.From actual problem,we can extractmany in…     

How serious is the modifiable areal unit problem for analysis of English census data?

Population data are often collected or presented for geographical areas which may have little or no connection to the processes generating the data. Such areal units are termed 'modifiable'. However analysis undertaken on such data is not independent of how these areal units are configured. Indeed, Openshaw (1984) and others have shown that the results of statistical analysis may differ wildly according to the scale and pattern of the areal units used. This phenomenon is called the modifiable areal unit problem (MAUP). It is clear that the MAUP exists, but far from clear about how often it occurs, how often it affects the conclusions from empirical data analysis, and in what contexts it makes most (or least) difference. British census data are well suited for investigating these issues, being available for different geographies which neatly nest within each other, and for a range of different variables of interest to central and local government and to many academic disciplines. This article is concerned with bivariate correlations (using Pearson's r) between pairs of variables. The aim is to see if any variables seem particularly liable to display MAUP effects, and if so, why. The conclusion is that MAUP in many cases makes little or no difference to the results, but there are some variable pairs where the effect is substantial.     

中国保险业发展的经验函数分析

在对数据统计口径进行调整的基础上，利用全国的时间序列数据分析城乡居民可支配收入、城乡居民储蓄存款余额、社会保险福利费、金融价格指数、居民活期存款利率及制度环境对中国保费收入的影响，得出中国保险业发展的经验函数，再用各地区的面板数据来分析中国保险业发展的地区差异性。研究发现：社会保障与商业保险之间没有相互替代关系；政府对保险业的政策支持力度不够；三大地区保险业发展呈不同类型，东部地区呈均衡发展型，中部地区呈收入拉动型，西部地区呈储蓄拉动型。     

基于独立源分析的过程监测及故障诊断方法

多元统计过程控制(MSPC)要求观测数据服从正态分布,而实际的工业过程数据大都不满足正态分布条件。独立源分析(ICA)是近几年才发展起来的一种新的统计方法,可以克服对数据分布的依赖。为此以ICA算法为核心,引入一种新型的过程监测及故障诊断方法。应用ICA提取独立源,利用I2图,Ie2图和SPE图进行故障检测,将变量重构图用于诊断故障。以三水箱系统为背景进行的实验研究,验证了该方法的有效性。     

复杂系统中统计相关性测量的熵方法研究

在熵方法定义的关联度系数法的基础上，提出了一种计算复杂系统统计相关的广义关联度系数法，并将其应用到生态经济区划和中医理论（齿痕舌出现的特点）中，进而证明了该方法的有效性、结果表明：广义关联度系数法在计算时不需要特定的数据，从而减小了数据的不确定性和计算量；既适用于线性的情况也适用于非线性的情况；复杂系统分类所需的判据减少，使复杂系统分类简单化；可以对系统变量（或子系统）之间的相关性进行定量的描述．     

Convergence in Distribution for Uncertain Random Sequences with Dependent Random Variables

Random variables and uncertain variables are respectively used to model randomness and uncertainty. While randomness and uncertainty always coexist in a same complex system. As an evolution of random variables and uncertain variables, uncertain random variable is introduced as a tool to deal with complex phenomena including randomness and uncertainty simultaneously. For uncertain random variables, a basic and important topic is to discuss the convergence of its sequence.Specifically, this paper focuses on studying the convergence in distribution for a sequence of uncertain random sequences with different chance distributions where random variables are not independent.And the result of this paper is a generalization of the existing literature. Relations among convergence theorems are studied. Furthermore, the theorems are explained by several examples.     

少自由度串联机器人仿真分析

研究了一种少自由度串联机器人精确速度控制方法。少自由度机器人末端可控变量n与关节变量相等，而不可控变量(6—n)是这些可控变量的线性组合。文章用反螺旋理论通过建立独立运动变量和关节变量的运动模型，使机器人末端可控变量与关节变量成一一对应关系。以4自由度机器人为例进行仿真分析，结果证明了改方法的有效性。     

基于PCA和最小二乘支持向量机的软测量建模

软测量技术是解决工业过程中普遍存在的一类难以在线测量变量估计问题的有效方法,支持向量机是基于统计学习理论的一种新的机器学习方法。提出了一种基于主元分析(PCA)和最小二乘支持向量机的软测量建模方法,用主元分析对输入变量进行数据压缩,消除变量之间的相关性,简化支持向量机结构,并通过交叉验证的方法对支持向量机进行参数选择。将其用于4-CBA软测量建模的结果表明:该方法具有学习速度快、跟踪性能好以及泛化能力强等优点,为4-CBA软测量建模的在线实施提供了方便。     

基于最大熵原理的多失效模式下煤巷锚杆支护结构体系可靠度模型

煤巷锚杆支护结构中包含多个相关的失效模式,传统的煤巷锚杆支护结构可靠度分析方法没有考虑多个失效模式之间的相关性,使得煤巷锚杆支护结构的可靠度被低估.为此,提出多失效模式下的煤巷锚杆支护结构分析方法,建立考虑多失效模式相关的煤巷锚杆支护结构体系可靠度分析模型.同时,采用最大熵原理推断煤巷锚杆支护结构参数的统计特征,利用对数正态分布描述岩石和煤体的粘聚力和内摩擦角.并采用Monte Carlo模拟法进行多失效模式下结构体系可靠度计算. 研究结果表明：采用最大熵原理能有效推断煤巷锚杆支护结构基本变量统计特征;多失效模式相关的结构可靠度模型所得到的可靠度值 比传统单一不相关模式下所计算的结果更加科学、准确;在MATLAB环境下采用Monte Carlo模拟法编程计算煤巷锚杆支护结构体系可靠度,无需将功能函数线性化,随机变量正态化,不需要求解近似联合密度函数,不需要进行复杂变换,编程过程简单,精度高.     

Bayesian empirical likelihood estimation of quantile structural equation models

Structural equation model (SEM) is a multivariate analysis tool that has been widely applied to many fields such as biomedical and social sciences. In the traditional SEM, it is often assumed that random errors and explanatory latent variables follow the normal distribution, and the effect of explanatory latent variables on outcomes can be formulated by a mean regression-type structural equation. But this SEM may be inappropriate in some cases where random errors or latent variables are highly nonnormal. The authors develop a new SEM, called as quantile SEM (QSEM), by allowing for a quantile regression-type structural equation and without distribution assumption of random errors and latent variables. A Bayesian empirical likelihood (BEL) method is developed to simultaneously estimate parameters and latent variables based on the estimating equation method. A hybrid algorithm combining the Gibbs sampler and Metropolis-Hastings algorithm is presented to sample observations required for statistical inference. Latent variables are imputed by the estimated density function and the linear interpolation method. A simulation study and an example are presented to investigate the performance of the proposed methodologies.     

不良贷款有无回收判别:一类可选变量的支持向量机方法

针对不良贷款有无回收判别问题中属性变量数目多、示性变量比例高的特点,提出了一类可选择变量的支持向量机方法进行判别预测.该方法一是将逐步回归的支持向量机思想应用在模型变量的选择上,二是将线性逐步回归的结果作为模型选择变量的初始状态,解决了传统支持向量机只能使用固定变量的问题. 实证结果显示,该方法不仅提高了样本外预测的正确率, 而且具有很好的稳健性.     

基于仿真的随机活动网络进度费用联合风险

针对复杂随机活动网络活动时间、费用随机性和相关性特点,采用蒙特卡罗方法随机抽取时间、费用样本,再利用乔列斯基因子分解法,将独立分布的时间和费用随机样本转化为相关的随机样本,建立了时间和费用为相关随机变量的随机活动网络仿真模型.通过算例结果的比较分析,说明新模型可以更准确地预测项目的风险概率,进行时间-费用交换分析以及进行项目工期和费用优化.     

偏最小二乘回归在刀具磨损试验建模中的应用

应用灰色关联度筛选变量，将样本变量筛选为部分样本变量和全部样本变量组合用于建模的自变量，以刀具后刀面磨损量作为因变量，对不同切削条件下铣削加工过程刀具后刀面磨损的多组实验数据，采用偏最小二乘回归分析方法，建立对所选自变量的偏最小二乘回归模型。结果表明，该方法提取的成分具有线性无关的特点，对刀具磨损有较好的解释能力，且利于建模和预测，同时可以消除输入因素的多重共线性。刀具磨损的回归模型计算出不同切削条件下刀具后刀面的磨损量，以全部样本变量所建立的模型预测效果更为理想。     

Detecting Change-Point via Saddlepoint Approximations

It's well-known that change-point problem is an important part of model statistical analysis. Most of the existing methods are not robust to criteria of the evaluation of change-point problem.In this article, we consider "mean-shift" problem in change-point studies. A quantile test of single quantile is proposed based on saddlepoint approximation method. In order to utilize the information at different quantile of the sequence, we further construct a "composite quantile test" to calculate the probability of every location of the sequence to be a change-point. The location of change-point can be pinpointed rather than estimated within a interval. The proposed tests make no assumptions about the functional forms of the sequence distribution and work sensitively on both large and small size samples,the case of change-point in the tails, and multiple change-points situation. The good performances of the tests are confirmed by simulations and real data analysis. The saddlepoint approximation based distribution of the test statistic that is developed in the paper is of independent interest and appealing.This finding may be of independent interest to the readers in this research area.     

New statistical model for radar HRRP target recognition

The mixture of factor analyzers (MFA) can accurately describe high resolution range profile (HRRP) statistical characteristics.But how to determine the proper number of the models is a problem.This paper develops a variational Bayesian mixture of factor analyzers (VBMFA) model.This procedure can obtain a lower bound on the Bayesian integral using the Jensen's inequality. An analytical solution of the Bayesian integral could be obtained by a hypothesis that latent variables in the model are independent.During computing the parameters of the model,birth-death moves are utilized to determine the optimal number of model automatically.Experimental results for measured data show that the VBMFA method has better recognition performance than FA and MFA method.     

一种电离层慢相径扰动提取与补偿改进算法

针对采用调频连续波(FMCW)体制的天波超视距雷达的应用场合,提出了一种电离层扰动(慢相径变化)补偿改进算法。该算法利用雷达回波谱中海浪在空间上的独立性来获取统计样本,因而在无需对雷达系统作任何改动的情况下,可获得对电离层扰动瞬时频率变化的统计估计。通过相位补偿有效地抑制了电离层扰动造成的多普勒谱展宽和频率漂移。给出了应用该方法的具体步骤,通过仿真实验证明该算法的有效性。     

基于动态建模方法的可靠性增长试验评定

运用动态建模方法对可靠性增长试验下可靠性参数的先验分布进行分析．在任务可靠度先验分布确定的基础上，结合产品的少量现场试验数据，利用Bayes方法对系统的可靠性增长试验结果进行分析．首先给出了可靠性增长分析的动态模型，然后运用历次阶段试验中的可靠性增长数据建立动态参数的递推估计模型．在此基础上，给出各阶段可靠性增长试验中可靠性参数的Bayes估计．针对液体火箭发动机寿命分布为Weibull分布的特点，对Weibull寿命型系统的可靠性增长试验进行评定．通过一个实际例子说明了该方法的有效性．     

AHP中判断矩阵的区间权重及其一致性检验

AHP中由判断矩阵导出排序权重时,传统的方法只能得到"点"权重向量。为使结果更具柔性,考虑求解判断矩阵的区间权重向量。本文通过建立线性规划模型实现了这一点。与此同时,模型的最优值反映了判断矩阵的不一致性,故可借此进行一致性检验。通过模拟计算,对该检验方法和传统的通过计算CR值的方法间的相关性进行了统计分析。结果表明,二者具有显著的相关性。最后给出算例分析。     

DOES INVESTOR SENTIMENT PREDICT STOCK RETURNS？ THE EVIDENCE FROM CHINESE STOCK MARKET

This paper examines the proxy variables of investor sentiment in Chinese stock market carefully, and tries to construct an investor sentiment index indirectly. We use cross correlation analysis to examine lead-lag relationship between the proxy variables and HS300 index. The results show that net added accounts （NAA）, SSE share turnover （TURN）, and closed-end fund discount （CEFD） are leading variables to stock market. The average first day return of IPOs （RIPO） and relative degree of active trading in equity market （RDAT） are contemporary variables, while number of IPOs （NIPO） is a lagging variable of stock market. Using the sentiment proxy variables with most possible leading order, and forward selection stepwise regression method, the empirical results on monthly stock returns reveal that three leading proxy variables can be used to form a sentiment index. And the out of sample tests prove that this sentiment index has good predictive power of Chinese stock market, and it is robust.     

基于独立成分分析的时间序列谱聚类方法

为了对时间序列数据进行聚类分析, 提出了一种基于独立成分分析的时间序列多路归一化割谱聚类方法, 并给出了利用独立成分分析对时间序列数据进行特征提取和降维的理论解释. 该方法首先利用独立成分分析对时间序列数据进行特征提取, 然后利用多路归一化割谱聚类方法完成对时间序列特征数据的聚类分析, 从而得到了一种新的基于特征的时间序列聚类方法. 为了验证该方法的可行性和有效性, 将其应用于仿真时间序列数据和实际的股票时间序列数据聚类分析中, 取得了较好的数值结果.