Evaluation of credit risk based on firm performance

This paper investigates whether productive inefficiency measured as the distance from the industry’s ‘best practice’ frontier is an important ex-ante predictor of business failure. We use samples of French textiles, wood and paper products, computers and R&D companies to obtain efficiency estimates for individual firms in each industry. These efficiency measures are derived from a directional technology distance function constructed empirically using non-parametric data envelopment analysis (DEA) methods. Estimating binary and ordered logit regression models we find that productive efficiency has significant explanatory power in predicting the likelihood of default over and above the effect of standard financial indicators.     

Parameter Estimation of Nonlinear Stochastic Differential Equations: Simulated Maximum Likelihood versus Extended Kalman Filter and Itô-Taylor Expansion

This article compares several estimation methods for nonlinear stochastic differential equations with discrete time measurements. The likelihood function is computed by Monte Carlo simulations of the transition probability (simulated maximum likelihood SML) using kernel density estimators and functional integrals and by using the extended Kalman filter (EKF and second-order nonlinear filter SNF). The relation with a local linearization method is discussed. A simulation study for a diffusion process in a double well potential (Ginzburg–Landau equation) shows that, for large sampling intervals, the SML methods lead to better estimation results than the likelihood approach via EKF and SNF. A second study using a nonlinear diffusion coefficient (generalized Cox–Ingersoll–Ross model) demonstrates that the EKF type estimators may serve as efficient alternatives to simple maximum quasilikelihood approaches and Monte Carlo methods.     

New maximum entropy-based algorithm for structural design optimization

A new algorithm based on nonlinear transformation is proposed to improve the classical maximum entropy method and solve practical problems of reliability analysis. There are three steps in the new algorithm. Firstly, the performance function of reliability analysis is normalized, dividing by its value when each input is the mean value of the corresponding random variable. Then the nonlinear transformation of such normalized performance function is completed by using a monotonic nonlinear function with an adjustable parameter. Finally, the predictions of probability density function and/or the failure probability in reliability analysis are achieved by looking the result of transformation as a new form of performance function in the classical procedure of maximum entropy method in which the statistic moments are given through the univariate dimension reduction method. In the proposed method, the uncontrollable error of integration on the infinite interval is removed by transforming it into a bounded one. Three typical nonlinear transformation functions are studied and compared in the numerical examples. Comparing with results from Monte Carlo simulation, it is found that a proper choice of the adjustable parameter can lead to a better result of the prediction of failure probability. It is confirmed in the examples that result from the proposed method with the arctangent transformation function is better than the other transformation functions. The error of prediction of failure probability is controllable if the adjustable parameter is chosen in a given interval, but the suggested value of the adjustable parameter can only be given empirically.     

Computations for the familial analysis of binary traits

For familial aggregation of a binary trait, one method that has been used is the GEE2 (generalized estimating equation) method corresponding to a multivariate logit model. We solve the complex estimating equations for the GEE2 method using an automatic differentiation software which computes the derivatives of a function numerically using the chain rule of the calculus repeatedly on the elementary operations of the function. Based on this, we are able to show in a simulation study that the GEE2 estimates are quite close to the maximum likelihood estimates assuming a multivariate logit model, and that the GEE2 method is computationally faster when the dimension or family size is larger than four.     

机械可靠性分析的高精度响应面法

通过对已有可靠性分析中的响应面法的研究,提出了一种高精度的响应面法,该方法通过迭代线性插值的策略,来保证确定响应面的抽样点比经典的响应面法更接近真实的极限状态方程,并且该方法通过序列线性插值的方法来控制抽样点与插值中心点的距离,保证随着插值中心点收敛于真实设计点,抽样点提供更多的关于设计点附近真实极限状态方程的信息,进而保证了收敛的响应面能够在设计点附近更好地拟合真实的极限状态方程,并得到高精度的失效概率计算结果．算例充分说明了所提方法的合理性与适用性．     

Default risk analysis via a discrete‐time cure rate model

Cure models represent an appealing tool when analyzing default time data where two groups of companies are supposed to coexist: those which could eventually experience a default (uncured) and those which could not develop an endpoint (cured). One of their most interesting properties is the possibility to distinguish among covariates exerting their influence on the probability of belonging to the populations’ uncured fraction, from those affecting the default time distribution. This feature allows a separate analysis of the two dimensions of the default risk: whether the default can occur and when it will occur, given that it can occur. Basing our analysis on a large sample of Italian firms, the probability of being uncured is here estimated with a binary logit regression, whereas a discrete time version of a Cox's proportional hazards approach is used to model the time distribution of defaults. The extension of the cure model as a forecasting framework is then accomplished by replacing the discrete time baseline function with an appropriate time‐varying system level covariate, able to capture the underlying macroeconomic cycle. We propose a holdout sample procedure to test the classification power of the cure model. When compared with a single‐period logit regression and a standard duration analysis approach, the cure model has proven to be more reliable in terms of the overall predictive performance. Copyright © 2013 John Wiley & Sons, Ltd.     

M5 model tree and Monte Carlo simulation for efficient structural reliability analysis

Practically, the performance of many engineering problems can be defined using a complex implicit limit state function. Approximation of the accurate failure probability is very time-consuming and inefficient based on Monte Carlo simulation (MCS) for complex performance functions. M5 model tree (M5Tree) model is robust approach for simulation and prediction phenomena, which provides ability to dealing with complex implicit problems by dividing them into smaller problems. By improving the efficiency of reliability method using accurate approximated failure probability, an efficient reliability method using the MCS and M5Tree is proposed to calibrate the performance function and estimate the failure probability, respectively. The superiorities including simplicity and accuracy of M5Tree meta-model are investigated to evaluate the actual performance function through five nonlinear complex mathematical and structural reliability problems. The proposed reliability method-based MCS and M5Tree improved the computational efforts for evaluating the performance function in reliability analysis. The M5Tree significantly increased the efficiency of reliability analysis with accurate failure probability.     

On the Brown–Proschan model when repair effects are unknown

A device is repaired after failure. The Brown–Proschan (BP) model assumes that the repair is perfect with probability p and minimal with probability (1−p). Theoretical results usually suppose that each repair effect (perfect or minimal repair) is known. However, this is not generally the case in practice. In this paper, we study the behavior of the BP model when repair effects are unknown. In this context, the main features of the failure process are derived: distribution functions of times between failures, failure intensity, likelihood function, etc. We propose to estimate the repair efficiency parameter p and the parameters of the first time to failure distribution with the likelihood function or equivalently the EM algorithm. We also propose to combine a moment estimation of the scale parameter and a maximum likelihood estimation of other parameters. Copyright © 2010 John Wiley & Sons, Ltd.     

Logit tree models for discrete choice data with application to advice-seeking preferences among Chinese Christians

Logit models are popular tools for analyzing discrete choice and ranking data. The models assume that judges rate each item with a measurable utility, and the ordering of a judge’s utilities determines the outcome. Logit models have been proven to be powerful tools, but they become difficult to interpret if the models contain nonlinear and interaction terms. We extended the logit models by adding a decision tree structure to overcome this difficulty. We introduced a new method of tree splitting variable selection that distinguishes the nonlinear and linear effects, and the variable with the strongest nonlinear effect will be selected in the view that linear effect is best modeled using the logit model. Decision trees built in this fashion were shown to have smaller sizes than those using loglikelihood-based splitting criteria. In addition, the proposed splitting methods could save computational time and avoid bias in choosing the optimal splitting variable. Issues on variable selection in logit models are also investigated, and forward selection criterion was shown to work well with logit tree models. Focused on ranking data, simulations are carried out and the results showed that our proposed splitting methods are unbiased. Finally, to demonstrate the feasibility of the logit tree models, they were applied to analyze two datasets, one with binary outcome and the other with ranking outcome.     

基于历史故障数据的租赁设备预防维护策略优化

针对租赁设备的特殊性,提出了一种周期预防维护策略模型。该策略综合考虑设备的当前维护周期、预防维护、小修以及惩罚机制等因素对维护成本的影响,从设备的当前维护周期出发,构造出故障率分布的平滑函数,以设备的历史故障数据信息为依据,使用最大似然估计解析方法对设备的故障率分布函数参数进行有效估计,建立以租赁企业维护成本最小化为目标的周期预防维护策略模型。最后是算例分析,研究表明,该策略符合租赁设备维护的实际情况,可为租赁企业提供有效的维护解决方案。     

Reliability analysis for Weibull distribution with homogeneous heavily censored data based on Bayesian and least-squares methods

The reliability for Weibull distribution with homogeneous heavily censored data is analyzed in this study. The universal model of heavily censored data and existing methods, including maximum likelihood, least-squares, E-Bayesian estimation, and hierarchical Bayesian methods, are introduced. An improved method is proposed based on Bayesian inference and least-squares method. In this method, the Bayes estimations of failure probabilities are focused on for all the samples. The conjugate prior distribution of failure probability is set, and an optimization model is developed by maximizing the information entropy of prior distribution to determine the hyper-parameters. By integrating the likelihood function, the posterior distribution of failure probability is then derived to yield the Bayes estimation of failure probability. The estimations of reliability parameters are obtained by fitting distribution curve using least-squares method. The four existing methods are compared with the proposed method in terms of applicability, precision, efficiency, robustness, and simplicity. Specifically, the closed form expressions concerning E-Bayesian estimation and hierarchical Bayesian methods are derived and used. The comparisons demonstrate that the improved method is superior. Finally, three illustrative examples are presented to show the application of the proposed method.     

基于面板logit模型的上市公司财务困境预测

目前关于财务困境预测的研究大多是局限于截面数据的静态计量和统计模型,忽视了公司的财务状况是不断变化的事实.为了揭示公司财务状况的变化过程,利用面板数据建立了panel logit概率模型.研究结果表明,panel logit模型在预测准确度方面优于普通的logit模型.     

Solving a large scale semi-definite logit model

This paper is concerned with an algorithm for solving a large scale semi-definite logit model which cannot be solved by an outer approximation (cutting plane) algorithm proposed earlier by one of the authors. Outer approximation algorithm can solve a problem with up to 10 financial attributes and 7,800 companies which is less than satisfactory from the viewpoint of failure discriminant analysis. The new algorithm can generate an approximately optimal solution for problems with over 14 attributes and 8,000 companies, by which the quality of failure discriminant analysis would be substantially improved.     

Asymptotic Properties of a Class of Mixture Models for Failure Data: The Interior and Boundary Cases

We analyse an exponential family of distributions which generalises the exponential distribution for censored failure time data, analogous to the way in which the class of generalised linear models generalises the normal distribution. The parameter of the distribution depends on a linear combination of covariates via a possibly nonlinear link function, and we allow another level of heterogeneity: the data may contain "immune" individuals who are not subject to failure. Thus the data is modelled by a mixture of a distribution from the exponential family and a "mass at infinity" representing individuals who never fail. Our results include large sample distributions for parameter estimators and for hypothesis test statistics obtained by maximising the likelihood of a sample. The asymptotic distribution of the likelihood ratio test statistic for the hypothesis that there are no immunes present in the population is shown to be "non-standard"; it is a 50-50 mixture of a chi-squared distribution on 1 degree of freedom and a point mass at 0. Our analysis clearly shows how "negligibility" of individual covariate values and "sufficient followup" conditions are required for the asymptotic properties.     

An adaptive multiple-Kriging-surrogate method for time-dependent reliability analysis

For accurately and efficiently estimating the time-dependent failure probability (TDFP) of the structure, a novel adaptive multiple-Kriging-surrogate method is proposed. In the proposed method, the multiple Kriging models with different regression trends (i.e., constant, linear and quadratic) are simultaneously constructed with the highest accuracy, on which the TDFP can be obtained. The multiple regression trends are adaptively selected based on the size of sample base, the maximum differences of multiple models and the global accuracy of multiple models. After that, the most suitable multiple regression trends are identified. The proposed method can avoid man-made subjectivity for regression trend in general Kriging surrogate method. Furthermore, better accuracy and efficiency will be obtained by the proposed multiple surrogates than just using a fixed regression model for some engineering applications. Five examples involving four applications with explicit performance function and one tone arch bridge under hurricane load example with implicit performance function are introduced to illustrate the effectiveness of the proposed method for estimating TDFP.     

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In collecting clinical data, data would be censored due to competing risks or patient withdrawal. The statistical inference for censoring data is always based on the assumption that the failure time and censoring time is independent. But in practice the failure time and censoring time are often dependent. Dependent censoring make the job to deal with censoring data more complicated. In this paper, we assume that the joint distribution of the failure time variable and censoring time variable is a function of their marginal distributions. This function is called a copula. Under prespecified copulas, the maximum likelihood estimators for cox proportional hazards models are worked out. Statistical analysis results are carried by simulations. When dependent censoring happens, the proposed method will do better than the traditional method used in independent situations. Simulation results show that the proposed method can get efficient estimations.     

基于时间相依Cox回归的动态财务预警模型及实证

本文以中小企业为研究对象,从偿债能力、盈利能力等财务因素,加之公司治理、宏观环境等非财务因素出发,利用共线性检验和时间相依Cox回归构建动态财务预警模型,并与经典的Cox模型、logit模型进行对比分析。本研究的特色有二:一是通过时间相依Cox回归模型,构建随时间而变化的预警指标数据与财务危机之间的函数关系。利用偏似然估计、Breslow估计量分别拟合回归系数和基准危险强度,构建财务预警模型,预测企业在未来一段时间内每个时间点上的财务危机概率。相比于基于传统Cox模型的预警研究仅用一期的截面数据建模,本研究考虑了预警指标的动态变化对财务风险的影响,涵盖了更多的历史信息,达到提高预警精度的目的。二是考虑第一类错误“危机企业判为正常”与第二类错误“正常企业判为危机”给投资者造成的损失差异,衡量预警的“错误成本”,以错误成本最低为目标,反推出财务正常和财务危机之间的预警阈值,实现了对财务危机发生与否的提前预警功能。经过实证,本研究的财务预警模型精度较高,尤其对财务危机企业的正确识别率达到75%。相较于传统的Cox回归、logit模型,危机企业的正确识别率更高、错误成本更低。盈利能力、公司治理水平是对企业财务风险影响最为显著的因素。     

删失截断情形下失效率变点模型的Bayes参数估计

通过添加部分缺失寿命变量数据,得到了删失截断情形下失效率变点模型相对简单的似然函数.讨论了所添加缺失数据变量的概率分布和随机抽样方法.利用Monte Carlo EM算法对未知参数进行了迭代.结合Metropolis-Hastings算法对参数的满条件分布进行了Gibbs抽样,基于Gibbs样本对参数进行估计,详细介绍了MCMC方法的实施步骤.随机模拟试验的结果表明各参数Bayes估计的精度较高.     

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.     

Hybrid control variates-based simulation method for structural reliability analysis of some problems with low failure probability

The safety analysis of systems with nonlinear performance function and small probability of failure is a challenge in the field of reliability analysis. In this study, an efficient approach is presented for approximating small failure probabilities. To meet this aim, by introducing Probability Density Function (PDF) control variates, the original failure probability integral was reformulated based on the Control Variates Technique (CVT). Accordingly, using the adaptive cooperation of the subset simulation (SubSim) and the CVT, a new formulation was offered for the approximation of small failure probabilities. The proposed formulation involves a probability term (resulting from a fast-moving SubSim) and an adaptive weighting term that refines the obtained probability. Several numerical and engineering problems, involving nonlinear performance functions and system-level reliability problems, are solved by the proposed approach and common reliability methods. Results showed that the proposed simulation approach is not only more efficient, but is also robust than common reliability methods. It also presents a good potential for application in engineering reliability problems.