判别分析方法在医学应用中的进展

本文对医学领域中判别分析方法的新进展做一综述,介绍了微阵列基因表达数据判别分析中偏最小二乘法降维、离散小波变换法降维、logitboost算法、随机森林、模糊核判别分析以及时间序列多元数据有序判别分析法、自身有变化规律数据的变系数logistic回归模型判别分析法的基本思想、算法和适用条件。     

基于MTALAB的神经网络判别模型

判别分析是判别样品所属类型的一种统计方法.利用M ATLAB提供的神经网络工具箱为基础,设计了一个三层BP神经网络判别模型,提出了一种进行判别分析的新方法,实例表明,利用BP神经网络建立的判别模型是进行判别分析的有效方法.是对研究分类问题的方法的扩充.     

基于主成分和Fisher判别的DNA序列分类方法北大核心

统计DNA序列中64种包含3个碱基字符串的频率,基于生物学知识,以此作为区分不同类别DNA序列的特征.对此频率数据使用主成分分析和Fisher判别两种方法进行数据降维操作,根据降维后的数据建立距离判别模型,用训练样本回判,检验模型判别效果,最后对未知类别序列进行判别归类,比较分类结果.     

基于主成分和Fisher判别的DNA序列分类方法

统计DNA序列中64种包含3个碱基字符串的频率,基于生物学知识,以此作为区分不同类别DNA序列的特征.对此频率数据使用主成分分析和Fisher判别两种方法进行数据降维操作,根据降维后的数据建立距离判别模型,用训练样本回判,检验模型判别效果,最后对未知类别序列进行判别归类,比较分类结果.     

基于R软件的Bayes判别分析在医学中的应用

Bayes判别在进行判别分析时考虑到各总体出现的先验概率、预报的先验概率及错判造成的损失,其判别效能优于其他判别方法.对Bayes判别方法详细介绍的基础上,利用R软件对一组舒张压和胆固醇数据分别进行Bayes判别分析、Fisher判别分析和基于距离的判别分析,对比三种不同方法下得到的判别结果,结果表明Bayes判别分析得到的分类结果精度较高,Bayes判别分析在医学领域有较好的应用前景.     

Bayes判别分析在医疗数据处理中的应用

本文利用判别分析的基本原理和方法,针对肝硬化医疗数据建立数学模型,然后利用SPSS16.0作为工具求解模型,得到了三个有意义的能判别归类的函数判别式。     

双重筛选逐步判别分类方法及其应用

本文提出一个新的多元统计方法:双重筛选逐步判别分类,其目的是解决已知模型样本较少时,如何进行两类样本判别分类的问题,将此方法用于地质学中对于有矿和无矿的判别,取得较好的应用效果。     

弹性判别分析在纸币鉴别中的分类应用

分类在许多领域都是重要问题,弹性判别分析是有效解决多类问题的分类方法.基于纸币的四个属性,应用这个方法来鉴别纸币的真伪.运用统计软件R可以得到:训练集的最高准确率达到99.64%,对应检测集的错误率为0.73%.同时,由于回归模型的多样性,弹性判别分析有多种形式.根据数据的特征可以提出适当的方法,对于纸币鉴别的数据集,最好的弹性判别分析的形式应用了带有适应选择项和样条光滑参数的加性模型.     

稀疏VAR在股票收益率研究的应用

向量自回归模型(VAR)广泛应用在对时间相依的多元时间序列建模中,但在高维数据建模中,自回归的系数膨胀可能导致噪音估计、不稳定的预测、解释上的困难等问题。在实际应用中,序列的真实模型往往具有稀疏性,因此运用稀疏VAR模型对高维时间序列进行建模,不仅可以解决高维数据带来的上述困难,也有利于寻找高维数据内在的真实模型。本文以10家公司的股票收益率为研究对象,采用3种不同的稀疏估计方法,不但分析了股票收益率之间的动态关系,而且通过实证分析展示了稀疏估计的优势。     

多标准等级判别模型在信用评级中的应用研究

在对目前我国信用评级方法应用现状分析的基础上,提出改进的多标准等级判别模型.并将该模型应用于商业银行信用风险评估中.通过对银行五级分类贷款样本的实证研究,证实了该判别模型的有效性和先进性.     

Projection-pursuit approach to robust linear discriminant analysis

Discriminant analysis plays an important role in multivariate statistics as a prediction and classification method. It has been successfully applied in many fields of work and research. As it happens with other multivariate methods, discriminant analysis is highly vulnerable to the presence of outliers that commonly occur in many real world data sets. The lack of robustness of the classical estimators on which the linear discriminant function is based is a severe disadvantage and several authors have worked to find efficient ways to prevent the damage that outliers can cause. This paper focuses on the projection-pursuit approach to discriminant analysis. The projection-pursuit estimators are described and theoretical properties are deduced and their relevance is highlighted. These include Fisher consistency, affine equivariance, partial influence functions and asymptotic distributions. Application to real data and a simulation study reveal the robustness of the projection-pursuit approach. In both analyses the data relates to a large number of variables, a situation that is becoming common when new technology is applied to data gathering.     

多指标面板数据融合聚类分析

针对多指标面板数据的样品分类和历史时期划分问题,从多元统计分析理论角度提出一个多指标面板数据的融合聚类分析方法。该方法改进了多指标面板数据的因子分析和系统聚类方法,依据Fisher有序聚类理论,构造了Frobenius范数形式的离差平方和函数,提出了多指标面板数据的有序聚类方法。实证结果表明,该方法能够满足系统分析的统一性要求,保证指标之间的不相关;能够克服时间维度上均值处理造成的偏误,信息损失较少;能够解决面板数据有序聚类的问题;弥补了单一分析的片面性和局限性。     

DEA and the discriminant analysis of ratios for ranking units

The purpose of this study is to develop a new method which provides for given inputs and outputs the best common weights for all the units that discriminate optimally between the efficient and inefficient units as pregiven by the Data Envelopment Analysis (DEA), in order to rank all the units on the same scale. This new method, Discriminant Data Envelopment Analysis of Ratios (DR/DEA), presents a further post-optimality analysis of DEA for organizational units when their multiple inputs and outputs are given. We construct the ratio between the composite output and the composite input, where their common weights are computed by a new non-linear optimization of goodness of separation between the two pregiven groups. A practical use of DR/DEA is that the common weights may be utilized for ranking the units on a unified scale. DR/DEA is a new use of a two-group discriminant criterion that has been presented here for ratios, rather than the traditional discriminant analysis which applies to a linear function. Moreover, non-parametric statistical tests are employed to verify the consistency between the classification from DEA (efficient and inefficient units) and the post-classification as generated by DR/DEA.     

A comparison of statistical methods for prenatal screening for Down syndrome

Currently, prenatal screening for Down Syndrome (DS) uses the mother's age as well as three biochemical markers for risk prediction. Risk calculations for the biochemical markers use a quadratic discriminant function. In this paper we compare several classification procedures to quadratic discrimination methods for biochemical-based DS risk prediction, based on data from a prospective multicentre prenatal screening study. We investigate alternative methods including linear discriminant methods, logistic regression methods, neural network methods, and classification and regression-tree methods. Several experiments are performed, and in each experiment resampling methods are used to create training and testing data sets. The procedures on the test data set are summarized by the area under their receiver operating characteristic curves. In each experiment this process is repeated 500 times and then the classification procedures are compared. We find that several methods are superior to the currently used quadratic discriminant method for risk estimation for these data. The implications of these results for prenatal screening programs are discussed.     

Penalized multinomial mixture logit model

Normal distribution based discriminant methods have been used for the classification of new entities into different groups based on a discriminant rule constructed from the learning set. In practice if the groups are not homogeneous, then mixture discriminant analysis of Hastie and Tibshirani (J R Stat Soc Ser B 58(1):155–176, 1996) is a useful approach, assuming that the distribution of the feature vectors is a mixture of multivariate normals. In this paper a new logistic regression model for heterogenous group structure of the learning set is proposed based on penalized multinomial mixture logit models. This approach is shown through simulation studies to be more effective. The results were compared with the standard mixture discriminant analysis approach using the probability of misclassification criterion. This comparison showed a slight reduction in the average probability of misclassification using this penalized multinomial mixture logit model as compared to the classical discriminant rules. It also showed better results when applied to practical life data problems producing smaller errors.     

Bayesian Nonparametric Modeling for Multivariate Ordinal Regression

Univariate or multivariate ordinal responses are often assumed to arise from a latent continuous parametric distribution, with covariate effects that enter linearly. We introduce a Bayesian nonparametric modeling approach for univariate and multivariate ordinal regression, which is based on mixture modeling for the joint distribution of latent responses and covariates. The modeling framework enables highly flexible inference for ordinal regression relationships, avoiding assumptions of linearity or additivity in the covariate effects. In standard parametric ordinal regression models, computational challenges arise from identifiability constraints and estimation of parameters requiring nonstandard inferential techniques. A key feature of the nonparametric model is that it achieves inferential flexibility, while avoiding these difficulties. In particular, we establish full support of the nonparametric mixture model under fixed cut-off points that relate through discretization the latent continuous responses with the ordinal responses. The practical utility of the modeling approach is illustrated through application to two datasets from econometrics, an example involving regression relationships for ozone concentration, and a multirater agreement problem. Supplementary materials with technical details on theoretical results and on computation are available online.     

基于多元统计分析的湖库水质富营养化程度评价模型及应用

利用多元统计中的主成份分析及判别分析方法 ,建立了一种新的湖库水质富营养化程度综合评价模型 ,并给出就我国十二个湖库的评价实例 ,实证分析的结果表明 :这是一种稳定性较好且切实有效的综合评价方法模型     

Characterization and Statistical Estimation of a Discriminant Space for Gaussian Mixtures

The problem of classification of a multivariate observation X drawn from a mixture of Gaussian distributions is considered. A linear subspace of the least dimension containing all information about the cluster structure of X is called a discriminant space (DS). Estimation of DS is based on characterizations of DS via projection pursuit with an appropriate projection index. An estimator of DS is obtained merely by applying the projection pursuit with the projection index replaced by its nonparametric estimator. We discuss the asymptotic behavior of the estimator obtained in this way.