Sums of weighted spacings and a test for the logistic distribution

A simple proof for a theorem of Csörgö and Révész (1981b and 1984) concerning sums of weighted spacings is given, The conditions of the theorem are relaxed. As an application, a goodness-of-fit test for the logistic distribution is proposed. The percentage points of the proposed test statistic are obtained by a simulation experiment.     

固定收益债券信用等级迁移的影响因素分析：基于财务指标的实证研究

固定收益债券的信用等级迁移问题日益引起投资者和监管者的关注,预测信用等级迁移需要找到关键指标。财务数据对企业未来业绩具有显著影响,可以反映运营企业的信用质量。当前信用等级发生迁移债券存在发行期限集中、行业特征明显、发债目的差异化等特点,通过构建Logistic模型对影响债券信用等级迁移的财务指标进行实证分析发现：偿债能力和盈利能力都对企业债的信用等级迁移具有显著影响,但是信用升级和信用降级分别对不同的财务指标敏感。发债企业要想提高债券信用等级,需提高盈利能力;投资者要想降低信用风险,应考虑减少甚至剔除投资组合中偿债能力发生显著负面变化的债券;监管者要想对发债企业进行更有效监管,需关注偿债能力指标以及主营业务利润率的变化。     

企业经营管理预警：主成分分析在logistic回归方法中的应用

logistic回归分析是度量企业信用风险的一种主流方法,它的假设比较符合经济现实和金融数据分布的特点。但是考虑到现阶段我国上市公司的信用数据具有的高维性和高相关性等特点对logistic分析产生的负面影响,本文在logistic分析中引入了能够有效降维和消除logistic方程共线性等问题的主成分分析,并对我国沪深两市上市公司的经营失败进行了实证研究,结果表明结合主成分分析法的logistic回归分析在模型解释和预测准确率等力面均优于简单的logistic分析。     

中国人口迁移与生育率关系研究

本文利用2000年人口普查数据,考察了中国人口迁移与生育率的关系。通过比较农村本地人口、城市本地人口和流动迁移人口三个人口群体在生育率上的差异,并进行多元统计分析,结果表明,流动迁移对生育率有着非常显著影响,城市外来人口的生育率不仅显著低于农村本地人口,而且也低于城市本地人口;远期流迁人口的生育率要低于近期流迁人口的生育率。中国人口迁移与生育率的关系出现了与已有的迁移生育率理论的不一致。1990年代中国的迁移生育率发生了转变。     

Improving logistic regression on the imbalanced data by a novel penalized log-likelihood function

Logistic regression is estimated by maximizing the log-likelihood objective function formulated under the assumption of maximizing the overall accuracy. That does not apply to the imbalanced data. The resulting models tend to be biased towards the majority class (i.e. non-event), which can bring great loss in practice. One strategy for mitigating such bias is to penalize the misclassification costs of observations differently in the log-likelihood function. Existing solutions require either hard hyperparameter estimating or high computational complexity. We propose a novel penalized log-likelihood function by including penalty weights as decision variables for observations in the minority class (i.e. event) and learning them from data along with model coefficients. In the experiments, the proposed logistic regression model is compared with the existing ones on the statistics of area under receiver operating characteristics (ROC) curve from 10 public datasets and 16 simulated datasets, as well as the training time. A detailed analysis is conducted on an imbalanced credit dataset to examine the estimated probability distributions, additional performance measurements (i.e. type I error and type II error) and model coefficients. The results demonstrate that both the discrimination ability and computation efficiency of logistic regression models are improved using the proposed log-likelihood function as the learning objective.     

中西部农村居民健康状况Logistic模型分析

运用有序Logistic模型分析了我国中西部农村居民的健康状况及其决定因素。研究发现,近年来我国中西部农村居民健康状况总体有所好转。中部地区的状况要好于西部地区。中老年人的健康水平下降,妇女的健康水平较差。中学教育对改善健康水平有积极影响。收入的增加和家庭环境卫生的改善有助于提高健康水平。建议政府继续加大对中西部地区农村合作医疗制度改革的支持力度,重视对农村基础教育和环境卫生设施的投入,采取措施维护中老年人和妇女群体的健康水平,改善落后地区的卫生设施和医疗保健条件,促进健康公平。     

Generalized linear models with functional predictors

Summary. We present a technique for extending generalized linear models to the situation where some of the predictor variables are observations from a curve or function. The technique is particularly useful when only fragments of each curve have been observed. We demonstrate, on both simulated and real data sets, how this approach can be used to perform linear, logistic and censored regression with functional predictors. In addition, we show how functional principal components can be used to gain insight into the relationship between the response and functional predictors. Finally, we extend the methodology to apply generalized linear models and principal components to standard missing data problems.     

Analysis of longitudinal multiple-source binary data using generalized estimating equations

Summary.  We present a multivariate logistic regression model for the joint analysis of longitudinal multiple-source binary data. Longitudinal multiple-source binary data arise when repeated binary measurements are obtained from two or more sources, with each source providing a measure of the same underlying variable. Since the number of responses on each subject is relatively large, the empirical variance estimator performs poorly and cannot be relied on in this setting. Two methods for obtaining a parsimonious within-subject association structure are considered. An additional complication arises with estimation, since maximum likelihood estimation may not be feasible without making unrealistically strong assumptions about third- and higher order moments. To circumvent this, we propose the use of a generalized estimating equations approach. Finally, we present an analysis of multiple-informant data obtained longitudinally from a psychiatric interventional trial that motivated the model developed in the paper.     

Modelling spatially correlated data via mixtures: a Bayesian approach

Summary. The paper develops mixture models for spatially indexed data. We confine attention to the case of finite, typically irregular, patterns of points or regions with prescribed spatial relationships, and to problems where it is only the weights in the mixture that vary from one location to another. Our specific focus is on Poisson-distributed data, and applications in disease mapping. We work in a Bayesian framework, with the Poisson parameters drawn from gamma priors, and an unknown number of components. We propose two alternative models for spatially dependent weights, based on transformations of autoregressive Gaussian processes: in one (the logistic normal model), the mixture component labels are exchangeable; in the other (the grouped continuous model), they are ordered. Reversible jump Markov chain Monte Carlo algorithms for posterior inference are developed. Finally, the performances of both of these formulations are examined on synthetic data and real data on mortality from a rare disease.     

Bayesian incorporation of repeated measurements in logistic discrimination

A common problem in medical statistics is the discrimination between two groups on the basis of diagnostic information. Information on patient characteristics is used to classify individuals into one of two groups: diseased or disease-free. This classification is often with respect to a particular disease. This discrimination has two probabilistic components: (1) the discrimination is not without error, and (2) in many cases the a priori chance of disease can be estimated. Logistic models (Cox 1970; Anderson 1972) provide methods for incorporating both of these components. The a posteriori probability of disease may be estimated for a patient on the basis of both current measurement of patient characteristics and prior information. The parameters of the logistic model may be estimated on the basis of a calibration trial. In practice, not one but several sets of measurements of one characteristic of the patient may be made on a questionable case. These measurements typically are correlated; they are far from independent. How should these correlated measurements be used? This paper presents a method for incorporating several sets of measurements in the classification of a case.