NBA季后赛成绩分析及预测：Logistic和Bayes模型

目的运用NBA常规赛数据统计分析季后赛球队,分析影响球队晋级的因素,预测判别球队晋级情况。方法因子分析对球队各项统计指标降维综合,提出了新的球队综合实力计算方法,根据NBA官方公式得到球员得分,结合主教练与主客场因素,建立Logistic模型与Bayes判别模型。结果新的球队综合实力计算方法优于官方公式;教练的执教能力对球队的晋级贡献最大;具有主场优势的球队只要获胜概率达到0.38则认为晋级;Logistic模型与Bayes判别模型判别正确率均较高。结论根据各指标建立的模型适用于所有季后赛球队,可用于预测季后赛晋级情况。     

信用评分模型综述

本文对信用评分领域大量的模型和方法以及相关文献做了细致的分类和综合比较,这些模型包括多元判别分析模型、数学规划法、Logistic回归分析和神经网络模型等。     

上市公司信用风险评估方法之比较

本文分别运用Logistic回归法和主成分判别分析法建立了两种模型,并比较两种模型的判别效率,从而确定一种好的评估上市公司信用风险的模型。     

我国制造业上市公司财务困境预警分析

文章选取制造业上市公司作为研究对象,应用Logistic回归分析法和Fisher判别分析法,分别构建了适用于制造业财务预警的模型,并针对模型的具体情况提出了一些建议。     

婚配概率及婚配对数估计方法的探讨

 估算独生子女和非独生子女之间婚配概率及婚配对数是生育政策仿真的关键技术之一。本文首次提出同龄概率法及多龄概率法,并对全国层面独生子女之间、独生子女与非独生子女之间、非独生子女之间的婚配概率及婚配对数进行了估算,详细阐述了两种方法的原理及运算步骤,并对两种方法的运算结果进行分析比较。结果表明,这两种方法都可以计算独生子女和非独生子女之间多种婚配概率,并能估算出各类婚配夫妇对数。其中,同龄概率法较直观,数据易取得, 但与实际存在一定的偏差;多龄概率法更接近于现实,受婚配对象人数突变的影响更小。     

分行业的企业财务危机预警模型比较研究

世界各国学者分别用不同的统计模型对信用风险进行全行业的实证研究。中国在此方面的研究尚处起步阶段。综合运用多元判别模型、Logistic模型、主成分模型,分不同行业对企业财务危机进行预警研究。比较分析了不同行业预警模型的判别准确率,不同预警技术的判别准确率,多年度预警的可行性,预警模型的稳定性,大类、中类行业预警的通用性等问题。商业银行可以使用这些模型进行信用风险度量和信贷风险预警。     

我国上市公司财务困境预测新探

本文采用主成分分析方法确定模型变量,建立多元判别分析(MDA)、Logistic回归和改进型BP神经网络模型进行财务困境预测。结果表明,神经网络模型的预测准确率明显优于多元判别分析和Logistic回归模型,而后两者的判别效果接近,神经网络模型更适合于财务困境预测。但三种模型的长期预警能力不够理想,提出建立以定量模型为主、定性分析为辅的上市公司财务困境预测新方法。     

一类违约概率测算模型的构建及验证

文章基于实证数据,建立了基于Logistic回归的农村合作金融机构零售客户的违约概率测算模型,结果表明,客户行业、婚姻状况、教育程度、年龄、客户性质等因子与违约概率显著相关.采用2011年新一期的零售客户数据对模型进行实际验证,模型判别的正确率为88.6％,违约概率测算模型对零售客户违约概率的预测有效.     

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。     

一次基于平均策略的判别财务危机试验

文章基于平均策略,使用BP神经网络对贝叶斯判别、费歇尔线性判别和logistic回归判别财务危机的输出新变量进行加权平均再判别,并和单一方法判别的效果比较。应用双层分类器做了一次财务危机判别的新尝试。     

数量化Ⅱ类弓形效应修正方法及应用

对应分析在对定性数据进行数量化处理过程中出现了“弓形效应”，关于对应分析的“弓形效应”的修正方法已经有了丰富的研究成果，避免了可能错误的分析结果，对理论界和应用领域都有重要意义。数量化Ⅱ类是关于定性数据的一种判别分析方法，在国内外已被广泛应用。本文通过大量模拟数据研究发现，数量化Ⅱ类在对定性数据进行数量化过程中出现了“弓形效应”，降低了正判别率，同时不能正确再现原始数据信息，得出与原始数据信息不符的错误分析结果，为修正“弓形效应”，提出了二阶段判别分析法，并从正判别率和对原始数据再现程度两个方面对数量化Ⅱ类与二阶段判别分析法进行了比较，同时将二阶段判别分析法运用到个人信用评级中，发现二阶段判别分析法的判别性能优于数量化Ⅱ类。     

A study on discriminant analysis techniques applied to multivariate lognormal data

The purpose of this paper is to examine the multiple group (>2) discrimination problem in which the group sizes are unequal and the variables used in the classification are correlated with skewed distributions. Using statistical simulation based on data from a clinical study, we compare the performances, in terms of misclassification rates, of nine statistical discrimination methods. These methods are linear and quadratic discriminant analysis applied to untransformed data, rank transformed data, and inverse normal scores data, as well as fixed kernel discriminant analysis, variable kernel discriminant analysis, and variable kernel discriminant analysis applied to inverse normal scores data. It is found that the parametric methods with transformed data generally outperform the other methods, and the parametric methods applied to inverse normal scores usually outperform the parametric methods applied to rank transformed data. Although the kernel methods often have very biased estimates, the variable kernel method applied to inverse normal scores data provides considerable improvement in terms of total nonerror rate.     

Probit and logistic discriminant functions

Most discriminant functions refer to qualitatively district groups. Talis et al. (1975) introduced the probit discriminant function for distinguishing between two ordered groups. They showed how to estimate this function for mixture sampling and continuous predictor variables. Here an estimation system is given for the more common separate sampling which is applicable to continuous and/or discrete predictor variables. When used solely with continuous variables) this method of estimation is more robust than Tallis!

The relationship of probit and logistic discrimination is discussed.     

Disoominkfrcn between gaussian time series based on their spectral differences

Discrimination between two Gaussian time series is examined assuming that the important difference between the alternative processes is their covarianoe (spectral) structure. Using the likelihood ratio method in frequency domain a discriminant function is derived and its approximate distribution is obtained. It is demonstrated that, utilizing the Kullbadk-Leibler information measure, the frequencies or frequency bands which carry information for discrimination can be determined. Using this, it is shown that when mean functions are equal, discrimination based on the frequency with the largest discrimination information is equivalent to the classification procedure based on the best linear discriminant, Application to seismology is described by including a discussion concerning the spectral ratio discriminant for underground nuclear explosion and natural earthquake and is illustrated numerically using Rayleigh wave data from an underground and an atmospheric explosions.     

A NEW APPROACH TO DISCRIMINATION AND CLASSIFICATION USING A HAUSDORFF TYPE DISTANCE

A new method of discrimination and classification based on a Hausdorff type distance is proposed. In two groups, the Hausdorff distance is defined as the sum of the furthest distance of the nearest elements of one set to another. This distance has some useful properties and is exploited in developing a discriminant criterion between individual objects belonging to two groups based on a finite number of classification variables. The discrimination criterion is generalized to more than two groups in a couple of ways. Several data sets are analysed and their classification accuracy is compared to that obtained from linear discriminant function and the results are encouraging. The method in simple, lends itself to parallel computation and imposes less stringent conditions on the data.     

On the Spectral Decomposition in Normal Discriminant Analysis

This article enlarges the covariance configurations, on which the classical linear discriminant analysis is based, by considering the four models arising from the spectral decomposition when eigenvalues and/or eigenvectors matrices are allowed to vary or not between groups. As in the classical approach, the assessment of these configurations is accomplished via a test on the training set. The discrimination rule is then built upon the configuration provided by the test, considering or not the unlabeled data. Numerical experiments, on simulated and real data, have been performed to evaluate the gain of our proposal with respect to the linear discriminant analysis.     

A robust logistic discrimination model

Logistic discrimination is a well documented method for classifying observations to two or more groups. However, estimation of the discriminant rule can be seriously affected by outliers. To overcome this, Cox and Ferry produced a robust logistic discrimination technique. Although their method worked in practice, parameter estimation was sometimes prone to convergence problems. This paper proposes a simplified robust logistic model which does not have any such problems and which takes a generalized linear model form. Misclassification rates calculated in a simulation exercise are used to compare the new method with ordinary logistic discrimination. Model diagnostics are also presented. The newly proposed model is then used on data collected from pregnant women at two district general hospitals. A robust logistic discriminant is calculated which can be used to predict accurately which method of feeding a woman will eventually use: breast feeding or bottle feeding.     

Discrete regularized discriminant analysis

A method of regularized discriminant analysis for discrete data, denoted DRDA, is proposed. This method is related to the regularized discriminant analysis conceived by Friedman (1989) in a Gaussian framework for continuous data. Here, we are concerned with discrete data and consider the classification problem using the multionomial distribution. DRDA has been conceived in the small-sample, high-dimensional setting. This method has a median position between multinomial discrimination, the first-order independence model and kernel discrimination. DRDA is characterized by two parameters, the values of which are calculated by minimizing a sample-based estimate of future misclassification risk by cross-validation. The first parameter is acomplexity parameter which provides class-conditional probabilities as a convex combination of those derived from the full multinomial model and the first-order independence model. The second parameter is asmoothing parameter associated with the discrete kernel of Aitchison and Aitken (1976). The optimal complexity parameter is calculated first, then, holding this parameter fixed, the optimal smoothing parameter is determined. A modified approach, in which the smoothing parameter is chosen first, is discussed. The efficiency of the method is examined with other classical methods through application to data.     

Classification of cyclical time series using complex demodulation

A new and innovative procedure based on time varying amplitudes for the classification of cyclical time series is proposed. In many practical situations, the amplitude of a cyclical component of a time series is not constant. Estimated time varying amplitudes obtained through complex demodulation of the time series are used as the discriminating variables in classical discriminant analysis. The aim of this paper is to demonstrate through simulation studies and applications to well-known data sets, that time varying amplitudes have very good discriminating power and hence their use in classical discriminant analysis is a simple alternative to more complex methods of time series discrimination.