协变量缺失情形下的逆概率加权众数回归估计

数据缺失在实际应用中普遍存在,数据缺失会降低研究效率,导致参数估计有偏.在协变量随机缺失(MAR)的假定下,本文基于众数回归和逆概率加权估计方法对线性模型进行参数估计.该方法结合参数Logistic回归和非参数Nadaraya-Watson估计两种倾向得分估计方法,分别构建IPWM-L估计量和IPWM-NW估计量.模拟研究和实例分析表明,众数回归模型比均值回归模型更具稳健性,逆概率加权众数(IPWM)估计方法在缺失数据下表现出了更好的拟合效果,与IPWM-L估计量相比, IPWM-NW估计量更稳健.     

因子分析在京杭大运河水质评价中的应用

用主成分分析的方法找出影响京杭大运河淮安段水质的主因子,求出因子得分函数,计算各样本的因子得分及水质综合评分,据此对京杭大运河淮安段各监测断面的水质进行评价.     

稳健统计(Ⅰ)

稳健统计是60年代兴起、80年代初初步定型的.笔者首次标触它时,很难理解它的统计思想.本讲座介绍稳健统计,不求理论上的系统性,只希望有助于理解稳健统计的基本概念及基本方法的统计思想. 全文分为三个部分:一是讲稳健统计的基本概念,分为第一、第二篇;二是介绍稳健回归;三是介绍多元分析中的稳健方法,主要是位置向量和协方差阵的稳健估计,以及稳健主成分分析.总共四篇.这里不涉及时间序列的稳健性问题 1.1关于基本假定 统计分析是在一定的基本假定下进行的.我们最熟悉的统计方法,诸如,样本均值估计总体均值μ,样本方差S~2=((X_1-X)~2+…+…     

基于因子分析和聚类分析的新疆各地区经济发展水平综合评价

建立经济发展水平综合评价指标体系,以新疆14个地州市为样本,运用因子分析方法进行实证分析,提取出综合经济实力因子、工业发展因子和农业发展因子3个主因子,并基于主因子得分矩阵对14个地州市进行聚类分析,聚类分析将新疆各地州市分为三类,并在此基础上得出了一些重要的启示.     

基于轮换样本连续性调查的校准组合估计方法研究

校准估计是抽样调查中比较常用的一种利用辅助信息提高估计量精度的方法。回归组合估计量作为轮换样本连续性调查中使用的一种有效的估计量,是可以通过校准程序得到的。基于回归组合估计量和校准程序之间的关系,本文提出了轮换样本连续性抽样调查条件下的不同校准组合估计量及其方差估计。校准组合估计量的主要思想是在校准估计程序中将拼配样本和非拼配样本的辅助信息进行不同的组合利用。本文利用美国现时人口调查的微观数据进行数值模拟,来比较不同校准组合估计量的估计效率,模拟结果表明两步校准组合估计量和两步校准双组合估计量的表现相似,且估计精度都高于H-T估计量及回归组合估计量;而两步校准组合估计量由于其简便性更适合应用于实践中。最后以我国农村住户连续性抽样调查为例,设计一套符合我国实际的轮换样本连续性调查方案,并将提出的校准组合估计量运用于估计阶段,为中国政府统计调查提供一定的借鉴和参考.     

纵向数据下广义估计方程估计

广义估计方程方法是一种最一般的参数估计方法,广泛地应用于生物统计、经济计量、医疗保险等领域.在纵向数据下,由于组间数据是相关的,为了提高估计的效率,广义估计方程方法一般需要考虑个体组内相关性.因此,大多数文献对个体组内的协方差矩阵进行参数假设,但假设的合理性及协方差矩阵估计的好坏对参数估计效率产生很大影响,同时参数假设也可能导致模型误判.针对纵向数据下广义估计方程,本文提出了改进的GMM方法和经验似然方法,并对给出的估计量建立了大样本性质.其中分块的思想,避免了对个体组内相关性结构进行假设,从这种意义上说,这种方法具有一定的稳健性.我们还通过两个模拟的例子,考察了文中提出估计量的有限样本性质.     

空间非参回归的变量选择

空间变系数回归模型是空间线性回归模型的重要推广,在实际中有广泛的应用.然而,这个模型的变量选择问题还没有解决.本文通过一般的M型损失函数将均值回归、中位数回归、分位数回归和稳健均值回归纳入同一框架下,然后基于B样条近似,提出一个能够同时进行变量选择和函数系数估计的自适应组内(adaptive group)L_r(r≥1)范数惩罚的M型估计量.新方法有几个显著的特点:(1)对异常点和重尾分布稳健;(2)能够兼容异方差性,允许显著变量集合随所考虑的分位点不同而变化;(3)兼顾了估计量的有效性和稳健性.在较弱假设条件下,建立了变量选择的oracle性质.随机模拟和实例分析验证了所提方法在有限样本时的表现.     

基于Topsis改进的因子分析模型在面板数据中的应用研究——以中国经济为例

针对传统因子分析只限于对截面数据进行分析研究存在的不足作了改进.通过建立基于Topsis法改进的因子分析模型对面板数据进行研究分析.以每一年的横截面数据因子综合得分最高和最低分别作为最优和最劣向量,通过Topsis法求出每个样本因子综合得分与最优因子方案接近程度.以中国加入WTO后的经济增长为例,用模型的最优因子方案接近程度来刻画各个省份2004年-2012年的经济发展状况,研究得到的结论是大部分省份与最优因子方案接近度较大.     

产业集群创新能力评价模型的比较研究

针对产业集群创新能力评价的一些复杂方法,以文献中的基于BP神经网络的产业集群创新能力评价模型作为比较对象,提出了两种评价模型:组合评价模型和主成分指数模型.前者将变异系数法和Topsis法组合使用,用以评价产业集群创业能力;后者则是对所有参评样本的评价指标进行主成分分析,以主成分的方差贡献率为权重,构建主成分综合指数,从而形成产业集群创新能力的综合评价指数模型.对这两个模型用来自比较对象模型的同一数据进行了验证,三个模型都得出了非常相近的结果,而这两种模型更具可操作性且易于解释,这两者相比,主成分分析的方法则更为简单易行.     

有辅助信息时有限总体分布函数的新估计量

本文提出两个新的估计量,利用观察数据中的总体辅助信息来估计有限总体分布函数,并通过两个人工总体的模拟实验,比较新的估计量、传统的估计量及Rao,Kover&Mantel(1990)提出的估计量的相对平均误差与相对标准差。结果表明,从相对标准差的角度分析,两个新的估计量有一个是四个估计量中精度最好的一个,另一个也有很好的表现;而且它们在模型有所偏差时都具备了较好的稳健性。     

Robust factor analysis

Our aim is to construct a factor analysis method that can resist the effect of outliers. For this we start with a highly robust initial covariance estimator, after which the factors can be obtained from maximum likelihood or from principal factor analysis (PFA). We find that PFA based on the minimum covariance determinant scatter matrix works well. We also derive the influence function of the PFA method based on either the classical scatter matrix or a robust matrix. These results are applied to the construction of a new type of empirical influence function (EIF), which is very effective for detecting influential data. To facilitate the interpretation, we compute a cutoff value for this EIF. Our findings are illustrated with several real data examples.     

回归系数的广义岭型主相关估计及其优良性

In this paper, we propose a new biased estimator of the regression parameters, the generalized ridge and principal correlation estimator. We present its some properties and prove that it is superior to LSE （least squares estimator）, principal correlation estimator, ridge and principal correlation estimator under MSE （mean squares error） and PMC （Pitman closeness） criterion, respectively.     

Research on Inference of Candidate Database Web Surveys Based on Superpopulation Pseudo Design and the Combined Sample

How to solve the inference problem of candidate database web surveys is an urgent problem to be solved in the development of web survey. In order to solve this problem, the inference method of non-probability sampling based on superpopulation pseudo design and the combined sample is proposed. A superpopulation model is firstly built up to construct pseudo weights for a survey sample of the web candidate database. The estimator of the population mean is then computed according to the combined sample composed of the survey sample of the web candidate database and a probability sample. The variance estimator of the population mean estimator is lastly derived according to the variance estimation theory of the superpopulation model. The Bootstrap and Jackknife methods are also used to compute the variance estimator. And all these variance estimation methods are compared. The research results show that the population mean estimator based on superpopulation pseudo design and the combined sample is better, and has higher efficiency than the estimator only using the probability sample and the weighted estimator only using the survey sample of the web candidate database. The variance estimator computed by using the VM1, VM2 and VM3 method are relatively better.     

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??How to solve the inference problem of candidate database web surveys is an urgent problem to be solved in the development of web survey. In order to solve this problem, the inference method of non-probability sampling based on superpopulation pseudo design and the combined sample is proposed. A superpopulation model is firstly built up to construct pseudo weights for a survey sample of the web candidate database. The estimator of the population mean is then computed according to the combined sample composed of the survey sample of the web candidate database and a probability sample. The variance estimator of the population mean estimator is lastly derived according to the variance estimation theory of the superpopulation model. The Bootstrap and Jackknife methods are also used to compute the variance estimator. And all these variance estimation methods are compared. The research results show that the population mean estimator based on superpopulation pseudo design and the combined sample is better, and has higher efficiency than the estimator only using the probability sample and the weighted estimator only using the survey sample of the web candidate database. The variance estimator computed by using the VM1, VM2 and VM3 method are relatively better.     

Variable selection in multivariate methods using global score estimation

A variable selection method using global score estimation is proposed, which is applicable as a selection criterion in any multivariate method without external variables such as principal component analysis, factor analysis and correspondence analysis. This method selects a subset of variables by which we approximate the original global scores as much as possible in the context of least squares, where the global scores, e.g. principal component scores, factor scores and individual scores, are computed based on the selected variables. Global scores are usually orthogonal. Therefore, the estimated global scores should be restricted to being mutually orthogonal. According to how to satisfy that restriction, we propose three computational steps to estimate the scores. Example data is analyzed to demonstrate the performance and usefulness of the proposed method, in which the proposed algorithm is evaluated and the results obtained using four cost-saving selection procedures are compared. This example shows that combining these steps and procedures yields more accurate results quickly.     

High breakdown estimators for principal components: the projection-pursuit approach revisited

Li and Chen (J. Amer. Statist. Assoc. 80 (1985) 759) proposed a method for principal components using projection-pursuit techniques. In classical principal components one searches for directions with maximal variance, and their approach consists of replacing this variance by a robust scale measure. Li and Chen showed that this estimator is consistent, qualitative robust and inherits the breakdown point of the robust scale estimator. We complete their study by deriving the influence function of the estimators for the eigenvectors, eigenvalues and the associated dispersion matrix. Corresponding Gaussian efficiencies are presented as well. Asymptotic normality of the estimators has been treated in a paper of Cui et al. (Biometrika 90 (2003) 953), complementing the results of this paper. Furthermore, a simple explicit version of the projection-pursuit based estimator is proposed and shown to be fast to compute, orthogonally equivariant, and having the maximal finite-sample breakdown point property. We will illustrate the method with a real data example.     

基于相关系数指标筛选法的油田集输泵机组用能评价体系研究

针对不同油田泵机组的用能情况不同而导致的泵机组评价指标种类和权重产生差异的问题,提出一种确定指标的方法,根据西北油田泵机组的实际工况,采用相关系数法筛选评价指标,再结合主成分分析法与灰色关联法综合评价泵机组的用能情况.结果表明筛选出了5个评价指标,按权重大小排序依次为泵机组效率、节流损失率、外输负载率、集输单耗、功率因数.通过关联度的计算,找到了能量损失严重的泵机组,并分析判断出其薄弱环节.     

The Distribution of Robust Distances

Mahalanobis-type distances in which the shape matrix is derived from a consistent, high-breakdown robust multivariate location and scale estimator have an asymptotic chi-squared distribution as is the case with those derived from the ordinary covariance matrix. For example, Rousseeuw's minimum covariance determinant (MCD) is a robust estimator with a high breakdown. However, even in quite large samples, the chi-squared approximation to the distances of the sample data from the MCD center with respect to the MCD shape is poor. We provide an improved F approximation that gives accurate outlier rejection points for various sample sizes.     

Robustifying principal component analysis with spatial sign vectors

In this paper, we apply orthogonally equivariant spatial sign covariance matrices as well as their affine equivariant counterparts in principal component analysis. The influence functions and asymptotic covariance matrices of eigenvectors based on robust covariance estimators are derived in order to compare the robustness and efficiency properties. We show in particular that the estimators that use pairwise differences of the observed data have very good efficiency properties, providing practical robust alternatives to classical sample covariance matrix based methods.     

A robust alternative to the ratio estimator under non-normality

In sampling theory, the traditional ratio estimator is the most common estimator of the population mean when the correlation between study and auxiliary variables is positively high. We introduce a new ratio-type estimator based on the order statistics of a simple random sample. We show that this new estimator is considerably more efficient than the traditional ratio estimator under non-normality, and remarkably robust to data anomalies such as presence of outliers in data sets.