Confidence sets and confidence bands for a beta distribution with applications to credit risk management

Incorporating statistical multiple comparisons techniques with credit risk measurement, a new methodology is proposed to construct exact confidence sets and exact confidence bands for a beta distribution. This involves simultaneous inference on the two parameters of the beta distribution, based upon the inversion of Kolmogorov tests. Some monotonicity properties of the distribution function of the beta distribution are established which enable the derivation of an efficient algorithm for the implementation of the procedure. The methodology has important applications to financial risk management. Specifically, the analysis of loss given default (LGD) data are often modeled with a beta distribution. This new approach properly addresses model risk caused by inadequate sample sizes of LGD data, and can be used in conjunction with the standard recommendations provided by regulators to provide enhanced and more informative analyses.     

Empirical likelihood inference for the accelerated failure time model

Accelerated failure time (AFT) models are useful regression tools for studying the association between a survival time and covariates. Semiparametric inference procedures have been proposed in an extensive literature. Among these, use of an estimating equation which is monotone in the regression parameter and has some excellent properties was proposed by Fygenson and Ritov (1994). However, there is a serious under-coverage problem for small sample sizes. In this paper, we derive the limiting distribution of the empirical log-likelihood ratio for the regression parameter on the basis of the monotone estimating equations. Furthermore, the empirical likelihood (EL) confidence intervals/regions for the regression parameter are obtained. We conduct a simulation study in order to compare the proposed EL method with the normal approximation method. The simulation results suggest that the empirical likelihood based method outperforms the normal approximation based method in terms of coverage probability. Thus, the proposed EL method overcomes the under-coverage problem of the normal approximation method.     

具有CF2=CF结构的化合物中19F NMR化学位移的计算

系统总结和分析前人对19F NMR化学位移研究成果的基础上,对19F NMR化学位移的规律进行研究,最终确定用回归分析中的最小二乘法来确定计算19F NMR化学位移的公式,并用F检验法对所得计算公式进行检验,给出了具有CF2=CF结构的化合物中19F NMR化学位移的计算公式δcal=B+△α+△β,该公式的置信度为9...     

数据统计处理中关于相关系数R的错误理解

本文旨在纠正一种在化学家中流传甚久的对统计数学中相关系数的错误理解.这种理解认为在数据拟合中单凭相关系数R大于某个人为指定值就可以判定数据拟合的优劣.     

A note on interval estimation of the standard deviation of a gamma population with applications to statistical quality control

Traditional process control charts for a measurement standard deviation are based on the assumption of normality, which may not always be valid. Assuming that measurements follow a gamma distribution, we have obtained an approximate distribution of the sample variance, scaled appropriately. This approximate distribution, which happens to be another gamma model, is used to derive an interval estimate of the population standard deviation. Further, the above approximate gamma model for the sample variance can be used to develop a process control chart as demonstrated by a simulated data set.     

The Accumulated Persistence Function,a New Useful Functional Summary Statistic for Topological Data Analysis,With a View to Brain Artery Trees and Spatial Point Process Applications

We start with a simple introduction to topological data analysis where the most popular tool is called a persistence diagram. Briefly, a persistence diagram is a multiset of points in the plane describing the persistence of topological features of a compact set when a scale parameter varies. Since statistical methods are difficult to apply directly on persistence diagrams, various alternative functional summary statistics have been suggested, but either they do not contain the full information of the persistence diagram or they are two-dimensional functions. We suggest a new functional summary statistic that is one-dimensional and hence easier to handle, and which under mild conditions contains the full information of the persistence diagram. Its usefulness is illustrated in statistical settings concerned with point clouds and brain artery trees. The supplementary materials include additional methods and examples, technical details, and the R code used for all examples.     

Empirical Likelihood Confidence Bands in Density Estimation

Abstract

Empirical likelihood methods are developed for constructing confidence bands in problems of nonparametric density estimation. These techniques have an advantage over more conventional methods in that the shape of the bands is determined solely by the data. We show how to construct an empirical likelihood functional, rather than a function, and contour it to produce the confidence bands. Analogs of Wilks's theorem are established in this infinite-parameter setting and may be used to select the appropriate contour. An alternative calibration, based on the bootstrap, is also suggested. Large-sample theory is developed to show that the bands have asymptotically correct coverage, and a numerical example is presented to demonstrate the technique. Comparisons are made with the use of bootstrap replications to choose both the shape and size of the bands.     

基于混合Ⅰ型删失数据的威布尔模型精确推断（英文）

威布尔分布是可靠性和寿命测试试验中常用的模型.本文中,我们考虑了基于混合Ⅰ型删失数据的威布尔模型精确推断.我们得到了威布尔分布未知参数最大似然估计的精确分布以及基于精确分布的置信区间.由于精确分布函数较为复杂,我们也给出了未知参数的另外几种置信区间,比如,基于近似方法的置信区间,Bootstrap置信区间.为了评价本文的方法,我们给出了一些数值模拟的结果.     

On the confidence preferences model

In this paper we study the model of decision under uncertainty consistent with confidence preferences. In that model, a decision maker held beliefs represented by a fuzzy set of priors and tastes captured by a standard affine utility index on consequences. First, we find some interesting properties concerning the well-known maxmin expected utility model, taking into account the point of view of the confidence preferences model. Further, we provide new examples of preferences that capture ambiguity-averse attitudes weaker than ambiguity attitudes featured by maxmin expected utility theory. Finally, we discuss the axiomatic foundations for the confidence preferences model with optimistic behavior.     

基于置信学习机与近红外光谱的煤种快速分类方法

基于近红外光漫反射谱技术的检测分析具有简单,快捷,安全等优势而被广泛应用于各行各业。应用近红外光谱分析技术实现不同煤种的快速分类,该方法可以替代费时费力费财的传统化学分析方法。同时首次将置信学习机(confidence machine)引入近红外分析中,实现了对分析结果的风险评估。采集了来自不同矿区共四种不同煤种(肥煤,焦煤,瘦煤和贫瘦煤)的199个煤样本的近红外光谱,通过机器学习的方法针对煤的近红外光谱构建了煤种分类器来实现煤种的快速分类。在近红外分析中引入了置信学习机的分析方式,结合支持向量机(SVM),构建了离线和在线的CM-SVM分类器。置信学习机是一种概率方法,使用概率(CM-SVM)来取代分类超平面(SVM)进行分类,不仅分类效果好于传统的SVM,达到了95.48%的分类率,还能同时给出每个样本分类结果的置信度,可靠度等风险信息。另外,CM-SVM通过对置信水平的设定,得到不同置信度下预测区间,该区间的预测正确率是与置信水平严格对应的,对于产品质量控制有非常重要的意义。置信学习机同时是一种在线的学习模型,新样本的不断加入会提高模型的性能,非常适合于工业现场的在线分析。在线的CM-SVM模型随着样本数的增加,预测结果的置信度有所提高,对工业现场近红外分析有重要意义。