基于Fisher变换的Bayes判别方法探索

判别分析是三大多元统计分析方法之一,在许多领域都有广泛的应用。通常认为距离判别、Fisher判别和Bayes判别是三种不同的判别分析方法,本文的研究表明,距离判别与Bayes判别是两种实质的判别方法,前者实际依据的是百分位点或置信区间,后者实际依据的是概率。而著名的Fisher判别,只是依据方差分析的思想,对判别变量进行线性变换,然后用于距离判别,其实不能算是一种实质的判别方法。本文将Fisher变换与Bayes判别结合起来,即先做Fisher变换,再利用概率最大原则做Bayes判别,得到一种新的判别途径,可进一步提高判别效率。理论与实证分析表明,基于Fisher变换的Bayes判别,适用场合广泛,判别效率最高。     

基于PLS对系统聚类分析方法的改进

1系统聚类方法及其存在的问题1.1系统聚类法为了将样本进行分类,就需要研究样本之间关系。目前用得最多的方法有两个:一种方法是用相似系数,比较相似的样本归为一类,不相似的样本归为不同的类。另一种方法是将一个样本看作P维空间的一个点,并在空间定义距离,距离较近的点归为一     

时间序列全局特征聚类分析方法及其应用

本文指出了用点和点距离度量时间序列相似性存在的问题,并给出一种新的相似性度量一全局特征,即从时间序列的统计分布特征、非线性和傅立叶频谱转换等3个方面提取全局特征构建特征向量,并进行聚类分析。本文以全国各地区人均GDP时间序列聚类为例,评估了距离相似法与全局特征法的聚类结果。实践证实全局特征法不但可以处理不同长度有缺失值的时序聚类,而且可以降低大型时间序列数据聚类计算的复杂度。     

第一HJ距离的理论分析

模型设定检验是资产定价的核心环节,作为模型误设的新指标,第一HJ距离受到学术界的广泛关注。然而,鲜有文献比较第一HJ距离和传统的误设测度的异同。本文系统地分析第一HJ距离的性质,并与传统的模型设定误差测度进行比较发现：（1）第一HJ距离将基于模型所用SDF的欧氏空间距离和最大定价误相联系,有丰富的经济含义;（2）第一HJ距离关注定价误差,相较于传统的模型误设测度,倾向于选择大的零Beta收益率和小的因子风险溢酬,对模型的排序有差异;（3）第一HJ距离的加权矩阵具有模型独立性和对测试资产组合选择的一致性。     

基于模糊C均值聚类法和粗糙集理论的评价方法研究

粗糙集理论为处理模糊、不完整、不确定性知识分析提供了一种新的分析理论,更具客观性,其不足之处在于决策表中的值必须是离散值.文章首先介绍了粗糙集理论及其基本概念;然后引入了基于模糊C均值聚类法的连续属性离散化方法,并结合二者提出了一种综合评价方法;最后以20家上市公司作为经验样本,对其财务状况做出了综合评价.     

Fisher多类判别分析法在期货价格预测中的应用

基于期货价格变化趋势的可预测性,利用判别分析中的Fisher多类判别模型,运用MATLAB程序语言编程,对期货交易中三月铜的数据进行分析,得到了判别函数,给出了预测判别准则,进一步讨论了其在期货价格预测中的应用。     

绩效图形理论及其实证

本文构造出一个基于系统定义的绩效概念空间,将员工绩效表达为在这个空间中分布的点,通过分析这些点的延伸、发展的特征,来分析绩效的整体特征。文章提出了完整的分析方法,称为绩效图形分析。最后,以某企业为样本进行实证研究。     

距离判别分析的应用

判别分析是一种在各种领域都有广泛应用的统计判别与分组的技术方法,文章对距离判别分析进行了具体的介绍,然后应用其解决实际问题。     

两总体的面板数据的距离判别分析方法

提出了根据距离之差的时序数据的趋势特征来考虑进行面板数据的判别分析,给出了重复观察的各时点间隔相同的情况时两总体的面板数据距离判别规则,并给出了距离之差的时序数据趋势特征的检验方法,最后分析了重复观察的各时点间隔并不相同时的距离判别分析方法.     

基于UML与灰色理论的指标体系构建

文章在构建指标体系时,先利用UML进行指标项选取、指标体系类模型构建;再通过灰色关联聚类方法对指标体系进行检验;并将这种方法用于构建农民工生活质量指标评价体系.     

Some Applications of the Rao Distance to Shrinkage Estimators

Bayesian statistics is concerned with how prior information influence inferences. This article studies this problem by comparing the value of the Rao distance between prior and posterior normal distributions. Particular cases include the linear Bayes estimator, the mixed estimator, and ridge-type estimators.     

边限检验理论及几点讨论

检验经济变量之间长期关系的协整技术要求变量是同阶单整的,这不可避免地涉及一定程度的预检验问题,而预检验问题会增加变量间长期关系分析的不确定性。当不能确定变量的单整类型时,边限检验理论提出了一个可以直接检验一个变量和一组解释变量之间长期关系的新方法。在介绍了边限检验方法中基本的VAR模型和假设及边限检验方法中用到的重要统计量——Wald统计量和T统计量及它们各自的渐近分布形式后,说明了边限检验理论在理论和实际运用当中需要注意的几个问题,最后通过实例分析说明了边限检验理论的运用。     

A Measure of Discrimination Between two Double Truncated Distributions

On the basis of Kullback-Leibler discrimination information, and of discrimination measures introduced by Ebrahimi and Kirmani (1996a) and by Di Crescenzo and Longobardi (2004), we propose a measure of discrepancy between double truncated distributions. Some properties of this measure are studied and some mistakes in the preceding literature are corrected.     

Discrimination analysis when the variates are grouped and observed in sequential order

Suppose that measurements Math', i = l,....,k, are consecutively taken on an individual at the prescribed costs C_i, i = l,....,k. the individual comes from one of the two populations H₁ and H₂, and it is desired to detect which population the individual belongs to. Given the loss incurreed in selecting population H_r when in fact it belongs to H_s, the prior probability P_r of H_r (r = 1,2), and assuming that H_r has the normal distribution N(µ_r, V), r = 1,2, we derive the sequential Bayesian solution of the discrimination problem when µ₁, µ₂ and V are known. When µ_r, V are unknown and must be estimated, we propose a solution which is asymptotic Bayesian with exponential convergence rate.     

On Using Hellinger Distance in Checking the Validity of Dynamic Approximations

The purpose of this article is to provide validation for the approximate algebraic propagation algorithms to accommodate non-Gaussian dynamic processes. These algorithms have been developed to carry out Bayesian analysis based on conjugate forms and presented with detailed examples of response distributions such as Poisson and Lognormal. The validity of the approximation algorithms can be checked by introducing a metric (Hellinger divergence measure) over the distribution of the states (parameters) and use it to judge the approximation. Theoretical bounds for the efficacy of such procedure are discussed.     

Describing the Dynamics of Attention to TV Commercials: A Hierarchical Bayes Analysis of the Time to Zap an Ad

This paper provides insights into the dynamics of attention to TV commercials via an analysis of the length of time that commercials are viewed before being 'zapped'. The model, which incorporates a flexible baseline hazard rate and captures unobserved heterogeneity across both consumers and commercials using a hierarchical Bayes approach, is estimated on two datasets in which commercial viewing is captured by a passive online device that continually monitors a household's TV viewing. Consistent with previous findings in psychology about the nature of attentional engagement in TV viewing, baseline hazard rates are found to be non-monotonic. In addition, the data show considerable ad-to-ad and household-to-household heterogeneity in zapping behavior. While one of the datasets contains some information on characteristics of the ads, these data do not reveal any firm links between the ad heterogeneity and the ad characteristics. A number of methodological and computational issues arise in the hierarchical Bayes analysis.     

A New Test of Randomness for Lehmer Generators Based on the Manhattan Distance Between Pairs of Consecutive Random Numbers

This article considers the Marsaglia effect by proposing a new test of randomness for Lehmer random number generators. Our test is based on the Manhattan distance criterion between consecutive pairs of random numbers rather than the usually adopted Euclidian distance. We derive the theoretical distribution functions for the Manhattan distance for both overlapping (two dimensional) as well as non-overlapping cases. Extensive goodness-of-fit testing as well as empirical experimentation provides ample proof of the merits of the proposed criterion.     

Some Limits in the Theory of Multicollinearity

The name “multicollinearity” was first introduced by Ragnar Frisch [2]. In his original formulation the economic variables are supposed to be composed of two parts, a systematic or “true” and an “error” component. There are at least two other cases when the same type of indeterminancy of the estimates arises due to different reasons. Considerable attention was given to this problem which arises when some or all the variables in a regression equation are highly inter-correlated and it becomes almost impossible to separate their influences and obtain the corresponding estimates of the regression coefficients. Consider a linear regression model     

On the distributions of the inner distance functions in the multivariate normal populations with unequal covariance matrices

The sample distance functions between an observation and a population were deduced by the likelihood procedures for discrimination problem in the case of several normal populations with unequal covariance matrices(1986). The present paper gives the exact MGFs of the distance functions for the case that the observation and the sample come from the same population and the limiting distributions of the distance functions by using the MCFs.     

Performance Evaluation Based on the Robust Mahalanobis Distance and Multilevel Modeling Using Two New Strategies

In this article, we propose a general framework for performance evaluation of organizations and individuals over time using routinely collected performance variables or indicators. Such variables or indicators are often correlated over time, with missing observations, and often come from heavy-tailed distributions shaped by outliers. Two new double robust and model-free strategies are used for evaluation (ranking) of sampling units. Strategy 1 can handle missing data using residual maximum likelihood (RML) at stage two, while strategy two handles missing data at stage one. Strategy 2 has the advantage that overcomes the problem of multicollinearity. Strategy one requires independent indicators for the construction of the distances, where strategy two does not. Two different domain examples are used to illustrate the application of the two strategies. Example one considers performance monitoring of gynecologists and example two considers the performance of industrial firms.