关于贸易周期的多维预警——多维指数构建及多维分析方法的应用

基于先行指标体系研究贸易周期,对于探测周期的拐点有重要的作用,进一步对出口、进口周期之间的关系以及出口、进口与经济周期之间的关系进行研究,将可以探测系统的拐点.然而,目前传统的景气分析方法只能针对一个经济周期进行分析,不能同时考虑多个周期的联动关系.而多维周期分析方法能够同时分析多个周期之间的动态关系及其演变过程,从而全面地反应经济周期的运行规律.本文首先对多维周期的分析方法进行了理论上的介绍;其次,运用FHLR方法构建了我国贸易周期的多维一致指数;然后,运用多维方法对贸易周期及其与重要经济变量的关系进行了多维分析,得出了一些重要结论.     

数据空间结构性及在KNN算法中的应用

数据空间结构性是多维数据客观存在的本征特征,是数据挖掘的重要内容.通过统计学的方法,分析多维数据空间属性变量和类型变量之间的结构特征,可以准确刻画数据在多维变量空间的相关性及其各向异性.数据空间结构特征可以用于机器学习算法的改进和提升,以提高模式识别的效果.融合了数据空间结构特征的KNN算法在稳定性和识别精度上均优于传统算法.通过在苏里格气田苏东41-33区块复杂碳酸盐岩的岩性识别中的应用表明,与传统KNN算法相比,数据空间结构的引入能提高识别准确率12.35%,并显示出算法的灵活性和适用性.多维数据空间结构的研究对机器学习算法的泛化能力和迁移性的提升等方面具有促进作用.     

定性资料的多元分析方法

本文首次引入定性资料分析的多元统计的方法,探讨了一些多样性指数与多元分布的协差阵的关系,由此导出了列联表分析的统计量。论证了两个定性变量之间的独立性与对应的多维随机向量的不相关性的关系,使得可以把多元分析中典型相关的处理方法移植到定性资料的分析,获得一些原有的统计量和一些新的统计量。     

基于样本协方差矩阵的多维随机数生成方法

对于概率模型未知的多维数据样本容量扩充问题,根据主成分分析原理以及多维正态分布的性质,讨论并给出了与已知多维样本数据有相同协方差结构的模拟数据生成算法,并在此基础上给出了变量的离散化处理方法。实现了在小样本数据基础上不改变变量间协方差结构的样本容量扩充,为小样本条件下的数学建模、检验和分析提供样本数据支撑。     

地区恶性肿瘤死亡率的对应分析

目的—了解山东省某县2000-2002年恶性肿瘤的地区分布和肿瘤类型分布特征.方法—应用分组对应分析对该县恶性肿瘤死亡资料进行分析.结果—得到各地区和各肿瘤类型的公因子及其负荷系数,并根据第一、二因子负荷系数绘制因子负荷平面图,可以清楚看出恶性肿瘤死亡率的聚集性及其高发地与低发地的分布.结论—将变量与样本结合起来的对应分析是对因子分析的有益补充,它可以分析二维数据阵的行因素与列因素之关系,达到研究目的.     

基于粗糙集理论的多维定性变量约简方法

基于粗糙集理论中的属性约简方法,提出了一种基于信息熵进行多维定性变量的约简方法,并进行了实证分析.     

上海市农村信息化公众满意度研究

文章在定性研究和数理检验的基础上开发了农村信息化公众满意度测量量表,并建立了农村信息化公众满意度指数模型.最后,依据上海郊区农村信息化调查数据,运用结构方程模型估计技术对测评模型进行了检验和参数求解.研究表明,文章建立的农村信息化公众满意度指数模型拟合度较高;另外,通过样本数据,得到了各潜在因子之间的路径系数以及可测变量的载荷系数,并对各潜在变量之间的相关关系进行了系统分析,文章在最后就研究发现的农村信息化过程不足提出了建议.     

中国投资与消费不均衡发展的实证研究:基于因子-Copula模型

在现有对投资与消费关系研究缺乏定量研究的基础上,引入Copula函数来探讨投资与消费的变动关系。首先利用因子分析进行投资与消费高维指标的降维处理,这样有效避免了Copula函数在多维变量下的建模复杂性;接着利用半参数建模方法选择了Cumbel函数来描述当前二者的关系;结果显示当前我国投资与消费存在显著不均衡关系,同时二者具有非对称性、非线性等数量特征;最后对上述研究结论进行了经济解释分析。     

双向聚类方法综述

传统的聚类方法由于无法提取样本和变量间的局部对应关系,并且当数据具有高维性和稀疏性时表现不佳,因此学者们提出了双向聚类,基于样本和变量间的局部关系,同时对样本和变量进行聚类,形成一系列子矩阵的聚类结果。近年来,双向聚类发展迅速,在基因分析、文本聚类、推荐系统等领域应用广泛。首先,对双向聚类方法进行梳理与归纳,重点阐述稀疏双向聚类、谱双向聚类和信息双向聚类三类方法,分析它们之间的区别和联系,并且介绍这三类方法在多源数据的整合分析、多层聚类、半监督学习以及集成学习上的发展现状和趋势;其次,重点介绍双向聚类在基因分析、文本聚类、推荐系统等领域的应用研究情况;最后,结合大数据时代的数据特征和双向聚类存在的问题,展望双向聚类未来的研究方向。     

基于复杂网络的时间序列单变量波动幅度研究

为研究时间序列单变量波动幅度演变规律,文章选择伦敦金下午收盘价格作为样本数据,借鉴统计物理学的方法进行研究.利用粗粒化方法建立了价格波动幅度变化模态,运用复杂网络理论对时间序列单变量波动幅度模态的统计、变化规律和演化规律进行了分析.研究结果表明,时间序列单变量波动幅度模态分布具有幂律性、群簇性和周期性,其波动幅度模态主要通过少数几种模态进行转换与演化.本研究方法不仅可以对不同类型时间序列单变量波动幅度进行研究,同时可为多变量波动幅度及其联动波动规律研究提供思路.     

On the exploration of linear latent effect for multivariate modeling

A data analysis method is proposed to derive a latent structure matrix from a sample covariance matrix. The matrix can be used to explore the linear latent effect between two sets of observed variables. Procedures with which to estimate a set of dependent variables from a set of explanatory variables by using latent structure matrix are also proposed. The proposed method can assist the researchers in improving the effectiveness of the SEM models by exploring the latent structure between two sets of variables. In addition, a structure residual matrix can also be derived as a by-product of the proposed method, with which researchers can conduct experimental procedures for variables combinations and selections to build various models for hypotheses testing. These capabilities of data analysis method can improve the effectiveness of traditional SEM methods in data property characterization and models hypotheses testing. Case studies are provided to demonstrate the procedure of deriving latent structure matrix step by step, and the latent structure estimation results are quite close to the results of PLS regression. A structure coefficient index is suggested to explore the relationships among various combinations of variables and their effects on the variance of the latent structure.     

Micro–macro multilevel latent class models with multiple discrete individual-level variables

An existing micro–macro method for a single individual-level variable is extended to the multivariate situation by presenting two multilevel latent class models in which multiple discrete individual-level variables are used to explain a group-level outcome. As in the univariate case, the individual-level data are summarized at the group-level by constructing a discrete latent variable at the group level and this group-level latent variable is used as a predictor for the group-level outcome. In the first extension, that is referred to as the Direct model, the multiple individual-level variables are directly used as indicators for the group-level latent variable. In the second extension, referred to as the Indirect model, the multiple individual-level variables are used to construct an individual-level latent variable that is used as an indicator for the group-level latent variable. This implies that the individual-level variables are used indirectly at the group-level. The within- and between components of the (co)varn the individual-level variables are independent in the Direct model, but dependent in the Indirect model. Both models are discussed and illustrated with an empirical data example.     

A bootstrap procedure for mixture models: applied to multidimensional scaling latent class models

A bootstrap procedure useful in latent class, or more general mixture models has been developed to determine the sufficient number of latent classes or components required to account for systematic group differences in the data. The procedure is illustrated in the context of a multidimensional scaling latent class model, CLASCAL. Also presented is a bootstrap technique for determining standard errors for estimates of the stimulus co‐ordinates, parameters of the multidimensional scaling model. Real and artificial data are presented. The bootstrap procedure for selecting a sufficient number of classes seems to correctly select the correct number of latent classes at both low and high error levels. At higher error levels it outperforms Hope's (J. Roy. Statist. Soc. Ser B 1968; 30 : 582) procedure. The bootstrap procedures to estimate parameter stability appear to correctly re‐produce Monte Carlo results. Copyright © 2002 John Wiley & Sons, Ltd.     

Latent models for cross-covariance

We consider models for the covariance between two blocks of variables. Such models are often used in situations where latent variables are believed to present. In this paper we characterize exactly the set of distributions given by a class of models with one-dimensional latent variables. These models relate two blocks of observed variables, modeling only the cross-covariance matrix. We describe the relation of this model to the singular value decomposition of the cross-covariance matrix. We show that, although the model is underidentified, useful information may be extracted. We further consider an alternative parameterization in which one latent variable is associated with each block, and we extend the result to models with r-dimensional latent variables.     

A latent variables approach for clustering mixed binary and continuous variables within a Gaussian mixture model

For clustering objects, we often collect not only continuous variables, but binary attributes as well. This paper proposes a model-based clustering approach with mixed binary and continuous variables where each binary attribute is generated by a latent continuous variable that is dichotomized with a suitable threshold value, and where the scores of the latent variables are estimated from the binary data. In economics, such variables are called utility functions and the assumption is that the binary attributes (the presence or the absence of a public service or utility) are determined by low and high values of these functions. In genetics, the latent response is interpreted as the ??liability?? to develop a qualitative trait or phenotype. The estimated scores of the latent variables, together with the observed continuous ones, allow to use a multivariate Gaussian mixture model for clustering, instead of using a mixture of discrete and continuous distributions. After describing the method, this paper presents the results of both simulated and real-case data and compares the performances of the multivariate Gaussian mixture model and of a mixture of joint multivariate and multinomial distributions. Results show that the former model outperforms the mixture model for variables with different scales, both in terms of classification error rate and reproduction of the clusters means.     

Bayesian Estimation of Discrete Multivariate Latent Structure Models With Structural Zeros

In multivariate categorical data, models based on conditional independence assumptions, such as latent class models, offer efficient estimation of complex dependencies. However, Bayesian versions of latent structure models for categorical data typically do not appropriately handle impossible combinations of variables, also known as structural zeros. Allowing nonzero probability for impossible combinations results in inaccurate estimates of joint and conditional probabilities, even for feasible combinations. We present an approach for estimating posterior distributions in Bayesian latent structure models with potentially many structural zeros. The basic idea is to treat the observed data as a truncated sample from an augmented dataset, thereby allowing us to exploit the conditional independence assumptions for computational expediency. As part of the approach, we develop an algorithm for collapsing a large set of structural zero combinations into a much smaller set of disjoint marginal conditions, which speeds up computation. We apply the approach to sample from a semiparametric version of the latent class model with structural zeros in the context of a key issue faced by national statistical agencies seeking to disseminate confidential data to the public: estimating the number of records in a sample that are unique in the population on a set of publicly available categorical variables. The latent class model offers remarkably accurate estimates of population uniqueness, even in the presence of a large number of structural zeros.     

Local cubic splines on non-uniform grids and real-time computation of wavelet transform

In this paper, local cubic quasi-interpolating splines on non-uniform grids are described. The splines are designed by fast computational algorithms that utilize the relation between splines and cubic interpolation polynomials. These splines provide an efficient tool for real-time signal processing. As an input, the splines use either clean or noised arbitrarily-spaced samples. Formulas for the spline’s extrapolation beyond the sampling interval are established. Sharp estimations of the approximation errors are presented. The capability to adapt the grid to the structure of an object and to have minimal requirements to the operating memory are of great advantages for offline processing of signals and multidimensional data arrays. The designed splines serve as a source for generating real-time wavelet transforms to apply to signals in scenarios where the signal’s samples subsequently arrive one after the other at random times. The wavelet transforms are executed by six-tap weighted moving averages of the signal’s samples without delay. On arrival of new samples, only a couple of adjacent transform coefficients are updated in a way that no boundary effects arise.     

Latent class analysis variable selection

We propose a method for selecting variables in latent class analysis, which is the most common model-based clustering method for discrete data. The method assesses a variable’s usefulness for clustering by comparing two models, given the clustering variables already selected. In one model the variable contributes information about cluster allocation beyond that contained in the already selected variables, and in the other model it does not. A headlong search algorithm is used to explore the model space and select clustering variables. In simulated datasets we found that the method selected the correct clustering variables, and also led to improvements in classification performance and in accuracy of the choice of the number of classes. In two real datasets, our method discovered the same group structure with fewer variables. In a dataset from the International HapMap Project consisting of 639 single nucleotide polymorphisms (SNPs) from 210 members of different groups, our method discovered the same group structure with a much smaller number of SNPs.