Bankruptcy prediction by generalized additive models

We compare several accounting‐based models for bankruptcy prediction. The models are developed and tested on large data sets containing annual financial statements for Norwegian limited liability firms. Out‐of‐sample and out‐of‐time validation shows that generalized additive models significantly outperform popular models like linear discriminant analysis, generalized linear models and neural networks at all levels of risk. Further, important issues like default horizon and performance depreciation are examined. We clearly see a performance depreciation as the default horizon is increased and as time goes by. Finally a multi‐year model, developed on all available data from three consecutive years, is compared with a one‐year model, developed on data from the most recent year only. The multi‐year model exhibits a desirable robustness to yearly fluctuations that is not present in the one‐year model. Copyright © 2006 John Wiley & Sons, Ltd.     

Robust Estimation of Tail Parameters for Two-Parameter Pareto and Exponential Models via Generalized Quantile Statistics

Robust estimation of tail index parameters is treated for (equivalent) two-parameter Pareto and exponential models. These distributions arise as parametric models in actuarial science, economics, telecommunications, and reliability, for example, as well as in semiparametric modeling of upper observations in samples from distributions which are regularly varying or in the domain of attraction of extreme value distributions. New estimators of generalized quantile type are introduced and compared with several well-established estimators, for the purpose of identifying which estimators provide favorable trade-offs between efficiency and robustness. Specifically, we examine asymptotic relative efficiency with respect to the (efficient but nonrobust) maximum likelihood estimator, and breakdown point. The new estimators, in particular the generalized median types, are found to dominate well-established and popular estimators corresponding to methods of trimming, least squares, and quantiles. Further, we establish that the least squares estimator is actually deficient with respect to both criteria and should become disfavored. The generalized median estimators manifest a general principle: smoothing followed by medianing produces a favorable trade-off between efficiency and robustness.     

Translation Ovoids of Generalized Quadrangles and Hexagnos

We define the notion of a translation ovoid in the classical generalized quadrangles and hexagons of order q, and we enumerate all known examples; translation spreads are defined dually. A modification of the known ovoids in the generalized hexagon H(q), q=3^2h+1, yields new ovoids of that hexagon. Dualizing and projecting along reguli, we obtain an alternative construction of the Roman ovoids due to Thas and Payne. Also, we construct a new translation spread in H(q) for any 1 mod 3, q odd, with the property that any projection along reguli yields the classical ovoid in the generalized quadrangle Q(4,q). Finally, we prove that for q odd, the new example is the only non-Hermitian translation spread in H(q) with the property that any projection along reguli yields the classical ovoid in Q(4,q).     

广义泊松回归模型的推广及其在医疗保险中应用

计数数据往往存在过离散(over-dispersed)即方差大于均值特征,若利用传统的泊松回归模型拟合数据往往会导致其参数的标准误差被低估,显著性水平被高估的错误结论。负二项回归模型、广义泊松回归模型通常被用来处理过离散特征数据。本文以两类广义泊松回归模型GP-1和GP-2模型为基础,将其推广为更为一般的GP-P形式,其中P为参数。此时,P=1或P=2,GP-P模型就退化为GP-1和GP-2模型。文中最后利用此类推广的GP-P模型处理了一组医疗保险数据,并与泊松回归模型、负二项回归模型拟合结果进行了比较。结果表明,推广后的GP-P模型的拟合效果更优。     

基于两阶段思想处理拒绝推断的信用评分模型

本文首先从数据缺失机制的角度分析了信用评分模型的开发和应用中所存在的样本偏差问题,提出了可以用拒绝推断来处理此类问题;然后在曾经被应用于拒绝推断问题处理的Heckman两阶段模型的基础上,提出了用拟似然两阶段模型和广义偏线性模型这两种新的两阶段方法来处理信用评分模型中的拒绝推断问题。经过实证分析发现,应用这两种方法可以得到很理想的结果。另外根据本文的研究,人行征信这类外部数据是拒绝推断最有效的方法,如果此类数据缺乏,则用拟似然两阶段模型和广义偏线性模型是比较有效的拒绝推断方法。     

Scale and time effects on mathematical models for transport in the environment

The purpose of this paper is to analyse mathematical models used in environmental modelling.Following a brief survey of the development in modelling scale-and time-dependent dispersion processes in the environment,this paper compares three similarity solutions,one of which is a solution of the generalized Feller equation(GF)with fractal parameters,and the other two for the newly-developed generalized Fokker-Planck equation(GFP).The three solutions are derived with parameters having physical significance.Data from field experiments are used to verify the solutions.The analyses indicate that the solutions of both GF and GFP represent the physically meaningful natural processes,and simulate the realistic shapes of tracer breakthrough curves.     

线性混合模型中方差分量的广义推断

本文考虑了线性混合模型中方差分量的假设检验和区间估计问题.基于广义P-值和广义置信区间的概念,构造了对应于随机效应的单个方差分量的精确检验和置信区间.所构造的广义p-值和广义置信区间是最小充分统计量的函数.对于两个独立线性混合模型中对应于随机效应的方差分量的比较,建立了精确检验和置信区间.进-步,研究了所给检验和置信区间的统计性质,给出了这些检验方法与文献中已有方法的功效比较的模拟结果.模拟结果表明,新检验在功效方面有显著的改进.最后,通过-个实例来演示本文方怯.     

Exponential family non-linear models for categorical data with errors of observation

We present a general framework for treating categorical data with errors of observation. We show how both latent class models and models for doubly sampled data can be treated as exponential family nonlinear models. These are extended generalized linear models with the link function substituted by an observationwise defined non-linear function of the model parameters. The models are formulated in terms of structural probabilities and conditional error probabilities, thus allowing natural constraints when modelling errors of observation. We use an iteratively reweighted least squares procedure for obtaining maximum likelihood estimates. This is faster than the traditionally used EM algorithm and the computations can be made in GLIM.¹ As examples we analyse three sets of categorical data with errors of observation which have been analysed before by Ashford and Sowden,² Goodman³ and Chen,⁴ respectively.     

非寿险分类费率模型的比较研究和实证分析

非寿险分类费率的厘定通常采用的方法有单项分析法、最小偏差法和广义线性模型,特别是后面两种方法在非寿险实务中应用十分广泛,精算文献中对这两种方法的理论和应用研究也较多,但对二者的比较研究较少。本文首先对最小偏差模型和广义线性模型进行了简要介绍,之后对这两种分类费率模型进行了系统的比较研究,总结了它们各自的优缺点以及二者之间的一些等价关系,最后通过一组实际的汽车保险数据讨论了它们的应用。     

Selection of smoothing parameters in<Emphasis Type="Italic">B</Emphasis>-spline nonparametric regression models using information criteria

We consider the use ofB-spline nonparametric regression models estimated by the maximum penalized likelihood method for extracting information from data with complex nonlinear structure. Crucial points inB-spline smoothing are the choices of a smoothing parameter and the number of basis functions, for which several selectors have been proposed based on cross-validation and Akaike information criterion known as AIC. It might be however noticed that AIC is a criterion for evaluating models estimated by the maximum likelihood method, and it was derived under the assumption that the ture distribution belongs to the specified parametric model. In this paper we derive information criteria for evaluatingB-spline nonparametric regression models estimated by the maximum penalized likelihood method in the context of generalized linear models under model misspecification. We use Monte Carlo experiments and real data examples to examine the properties of our criteria including various selectors proposed previously.     

基于加速失效时间模型模拟生存时间应用于检测生存性状位点

对于考察预指定情形下的统计模型的性能、性质及适应性,模拟研究是非常重要的统计工具.作为生存分析中两个最受欢迎的模型之一,由于加速失效时间模型中的因变量是生存时间的对数,且此模型能够以线性形式回归带有易解释的参数的协变量,从而加速失效模型比COX比例风险模型更便于拟合生存数据.首先提出了关于带有广义F-分布的加速失效模型的模拟研究中生成生存时间的方法,然后给出了描述加速失效时间模型的误差分布和相应的生存时间之间的一般的关系式,并给出了广义F-分布是如何生成生存时间的.最后,为证实所建议模拟技术的性能和有效性,将此方法应用于检测生存性状位点的模型中.     

Multivariate count data generalized linear models: Three approaches based on the Sarmanov distribution

Starting from the question: What is the accident risk of an insured individual?, we consider that the customer has contracted policies in different insurance lines: motor and home. Three models based on the multivariate Sarmanov distribution are analyzed. Driven by a real data set that takes into account three types of accident risks, two for motor and one for home, three trivariate Sarmanov distributions with generalized linear models (GLMs) for marginals are considered and fitted to the data. To estimate the parameters of these three models, we discuss a method for approaching the maximum likelihood (ML) estimators. Finally, the three models are compared numerically with the simpler trivariate Negative Binomial GLM and with elliptical copula based models.     

Submanifolds of constant sectional curvature in Pseudo-Riemannian manifolds

The generalized equation and the intrinsic generalized equation are considered. The solutions of the first one are shown to correspond to Riemannian submanifolds M ⁿ (K) of constant sectional curvature of psedo-Riemannian manifolds % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaaca% WGnbaaamaaDaaaleaaieGacaWFZbaabaGaaGOmaiaad6gacqGHsisl% caaIXaaaaOGaaiikamaanaaabaGaam4saaaacaGGPaaaaa!3D97!\[\overline M _s^{2n - 1} (\overline K )\] of index s, with % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4saiabgc% Mi5oaanaaabaGaam4saaaaaaa!3965!\[K \ne \overline K \], flat normal bundle and such that the normal principal curvatures are different from % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4saiabgk% HiTmaanaaabaGaam4saaaaaaa!388B!\[K - \overline K \]. The solutions of the intrinsic generalized equation correspond to Riemannian metrics defined on open subsets of R ⁿ which have constant sectional curvature. The relation between solutions of those equations is given. Moreover, it is proven that the submanifolds M under consideration are determined, up to a rigid motion of % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaaca% WGnbaaaaaa!36D0!\[\overline M \], by their first fundamental forms, as solutions of the intrinsic generalized equation. The geometric properties of the submanifolds M associated to the solutions of the intrinsic generalized equation, which are invariant under an (n – 1)-dimensional group of translations, are given. Among other results, it is shown that such submanifolds are foliated by (n – 1)-dimensional flat submanifolds which have constant mean curvature in M. Moreover, each leaf of the foliation is itself foliated by curves of % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaaca% WGnbaaaaaa!36D0!\[\overline M \] which have constant curvatures.     

Regular graphs constructed from the classical generalized quadrangle Q(4, q)

Let c_k be the smallest number of vertices in a regular graph with valency k and girth 8. It is known that c_{k + 1}?2(1 + k + k² + k³) with equality if and only if there exists a finite generalized quadrangle of order k. No such quadrangle is known when k is not a prime power. In this case, small regular graphs of valency k + 1 and girth 8 can be constructed from known generalized quadrangles of order q>k by removing a part of its structure. We investigate the case when q = k + 1 is a prime power, and try to determine the smallest graph under consideration that can be constructed from a generalized quadrangle of order q. This problem appears to be much more difficult than expected. We have general bounds and improve these for the classical generalized quadrangle Q(4, q), q even. © 2010 Wiley Periodicals, Inc. J Combin Designs 19:70‐83, 2010     

两类Cayley的向图的同构问题

证明了对m=1,2,3,有限广义双循环群B(Q8)是m-DCI群当且仅当它的极大交换子群L是m-DCI群且4|-1mm|L|;有限广义二面体群D是m-DCI群当且仅当它的极大交换子群K是m-DCI群且2|-1mm|K|.     

GLMMLasso: An Algorithm for High-Dimensional Generalized Linear Mixed Models Using ℓ1-Penalization

We propose an ?₁-penalized algorithm for fitting high-dimensional generalized linear mixed models (GLMMs). GLMMs can be viewed as an extension of generalized linear models for clustered observations. Our Lasso-type approach for GLMMs should be mainly used as variable screening method to reduce the number of variables below the sample size. We then suggest a refitting by maximum likelihood based on the selected variables only. This is an effective correction to overcome problems stemming from the variable screening procedure that are more severe with GLMMs than for generalized linear models. We illustrate the performance of our algorithm on simulated as well as on real data examples. Supplementary materials are available online and the algorithm is implemented in the R package glmmixedlasso.     

半参数广义线性混合效应模型的估计及其渐近性质

半参数广义线性混合效应模型在心理学、生物育种、医学等领域有广泛的应用. Zhang(1998)用最大惩罚似然函数的方法(MPLE)对模型的参数和非参数部分进行了估计, 而Zhang (1998) MPLE方法只适用于正态数据模型. 对于泊松等常用的模型, 常的方法是将随机效应看作缺失数据, 再引入EM算法. 本文基于McCulloch 1997)提出的MCNR算法, 此算法推广到半参数广义线性混合效应模型中并得到相应的估计算法. 于非参数部分, 本文采用P样条拟合并利用GCV方法选取光滑参数, 时证明了所得估计的相合性和渐近正态性. 最后, 过模拟和实例与其它算法作比较验证本文估计方法的有效性.     

变系数广义线性模型及其估计

本文以经典广义线性模型为基础,通过假定其中的回归变量的系数是某一度量空间中点的任意函数,提出了一类有广泛应用背景的变系数广义线性模型,增加了模型的灵活性和适应性,同时也适用于空间数据的统计分析。基于局部加权最大似然估计方法,文章讨论了变系数广义线性模型的拟合与统计推断,以及与之相关的局部权系统和其中光滑参数的确定。     

Jordan generalized derivations on triangular algebras

Let 𝒜 be a unital algebra and let ? be a unitary 𝒜-bimodule. We consider Jordan generalized derivations mapping from 𝒜 into ?. Our results on unitary algebras are applied to triangular algebras. In particular, we prove that any Jordan generalized derivation of a triangular algebra is a generalized derivation.     

基于伽玛与对数正态分布假设下的广义线性模型的比较和应用

本文在假设每次损失金额的变异系数相同,且它们服从伽玛分布或对数正态分布的条件下,讨论了加法模型和乘法模型的参数估计和拟合优度检验,并应用一组实际损失数据对上述模型进行了实证比较。结果表明,对于一组特定的损失数据,对数正态分布假设下的广义线性模型可能优于伽玛分布假设下的广义线性模型。