Multivariate Limited Translation Hierarchical Bayes Estimators

Based on the notion of predictive influence functions, the paper develops multivariate limited translation hierarchical Bayes estimators of the normal mean vector which serve as a compromise between the hierarchical Bayes and maximum likelihood estimators. The paper demonstrates the superiority of the limited translation estimators over the usual hierarchical Bayes estimators in terms of the frequentist risks when the true parameter to be estimated departs widely from the grand average of all the parameters.     

多元Copula密度估计的小波局部阈值方法

为了量化资产之间相依结构的局部特征,本文将小波阈值规则引入Copula参数估计,提出多元Copula密度的小波局部阈值估计量,发现Copula密度的光滑度指数、维数和采样容量是影响估值精度的重要因素,这一点也得到了以正态Copula为仿真算例的支持。本方法增强了参数Copula建模的局部自适应能力,进而有助于改进资产的市场风险估值与最优化配置。     

Copulas with maximum entropy

We shall find a multi-dimensional checkerboard copula of maximum entropy that matches an observed set of grade correlation coefficients. This problem is formulated as the maximization of a concave function on a convex polytope. Under mild constraint qualifications we show that a unique solution exists in the core of the feasible region. The theory of Fenchel duality is used to reformulate the problem as an unconstrained minimization which is well solved numerically using a Newton iteration. Finally, we discuss the numerical calculations for some hypothetical examples and describe how this work can be applied to the modelling and simulation of monthly rainfall.     

Minimax Hierarchical Empirical Bayes Estimation in Multivariate Regression

The multivariate normal regression model, in which a vector y of responses is to be predicted by a vector x of explanatory variables, is considered. A hierarchical framework is used to express prior information on both x and y. An empirical Bayes estimator is developed which shrinks the maximum likelihood estimator of the matrix of regression coefficients across rows and columns to nontrivial subspaces which reflect both types of prior information. The estimator is shown to be minimax and is applied to a set of chemometrics data for which it reduces the cross-validated predicted mean squared error of the maximum likelihood estimator by 38%.     

具有n次多项式截面的Copula函数

本文构造一类具有n次多项式截面的Copula函数C(x,y),并给出了C(x,y)是Copula函数的两个充分必要条件,同时推导出此类Copula函数的若干性质,包括对称性和相关度量等.     

改进的pair-copula参数估计方法在经济研究中的应用

对于pair-copula中的参数估计,大多假设copula函数的参数和条件变量独立,将参数简化成一个不依赖于条件变量的常数.本文假设copula函数的参数和条件变量不独立,该参数是以条件变量为自变量的一元函数.应用该方法实证分析了“克强指数”三个指标铁路货运量、工业用电量和贷款发放量的对数增长率之间的关系,研究发现该方法优于简化的pair-copula参数估计,并且得出在固定铁路货运量不变时,工业用电量和银行贷款发放量成负相关关系,且这种负相关性随铁路货运量增加而减弱.     

Focal Copulas: A Common Framework for Various Classes of Semilinear Copulas

Mediterranean Journal of Mathematics - A new method to construct semi-copulas is introduced. These semi-copulas are called focal semi-copulas and their construction is based on linear interpolation...     

两类特殊的联系函数(Copula)

提出两类联系函数,它们是阿基米德联系函数与F réchet-Hoeffd ing界的融合,是正序簇.一类介于F réchet-Hoeffd ing下界与一个特殊的联系函数之间;另一类介于F réchet-Hoeffd ingshang上界与一个特殊的联系函数之间.本文最后提出几个有待解决的问题.     

Operator Tail Dependence of Copulas

A notion of tail dependence based on operator regular variation is introduced for copulas, and the standard tail dependence used in the copula literature is included as a special case. The non-standard tail dependence with marginal power scaling functions having possibly distinct tail indexes is investigated in detail. We show that the copulas with operator tail dependence, incorporated with regularly varying univariate margins, give rise to a rich class of the non-standard multivariate regularly varying distributions. We also show that under some mild conditions, the copula of a non-standard multivariate regularly varying distribution has the standard tail dependence of order 1. Some illustrative examples are given.     

Copulas and associated fractal sets

The problem of constructing copulas whose supports are fractals has been studied by Fredricks, Nelsen and Rodríguez-Lallena [G.A. Fredricks, R.B. Nelsen, J.A. Rodríguez-Lallena, Copulas with fractal supports, Insurance Math. Econom. 37 (1) (2005) 42–48]. In this paper we continue on the path traced by these authors. We provide different types of families of self-similar copulas using techniques from Probability and Ergodic Theory to give properties on subsets of their fractal supports. In particular, we give new examples for those copulas and we analyze related topics with mutual singularity of the associated measures, Hausdorff dimension, and the connectedness of their supports.     

Computing the Volume of n-Dimensional Copulas

Abstract

A problem that is very relevant in applications of copula functions to finance is the computation of the survival copula, which is applied to enforce multivariate put–call parity. This may be very complex for large dimensions. The problem is a special case of the more general problem of volume computation in high-dimensional copulas. We provide an algorithm for the exact computation of the volume of copula functions in cases where the copula function is computable in closed form. We apply the algorithm to the problem of computing the survival of a copula function in the pricing problem of a multivariate digital option, and we provide evidence that this is feasible for baskets of up to 20 underlying assets, with acceptable CPU time performance.     

Copulas: Tales and facts

“But he does not wear any clothes” said the little child in Hans Christian Andersen’s “The Emperor’s New Clothes.”Mikosch’s research is partially supported by the Danish Research Council (SNF) GrantNo 21-04-0400. This is a discussion paper which was initiated at the 4th InternationalConference on Extreme Value Analysis in Gothenburg, 15–19 August, 2005; see.     

Optimal Bounds for Integrals with Respect to Copulas and Applications

We consider the integration of two-dimensional, piecewise constant functions with respect to copulas. By drawing a connection to linear assignment problems, we can give optimal upper and lower bounds for such integrals and construct the copulas for which these bounds are attained. Furthermore, we show how our approach can be extended in order to approximate extremal values in very general situations. Finally, we apply our approximation technique to problems in financial mathematics and uniform distribution theory, such as the model-independent pricing of first-to-default swaps.     

配备FGM Copulas二维随机向量之和的相依性

本文研究了配备Farlie-Gumbel-Morgenstern Copulas的二维随机向量之和的相依性,得到了在这类Copulas函数下两个独立的随机向量之和的Kendall及Spearman相依系数的一般公式;并针对边缘分布分别为指数分布的情况推导出了具体的公式;证明了当边缘分布满足一定的条件时,不存在尾部相依性.此外,对于几种不同边缘分布的情况进行了随机模拟与比较.这些方法及结果对两个企业(公司)合并后某两个随机指标之间的相依性问题的研究具有理论指导意义,为这类问题的进一步探索提供了理论基础.     

Copula函数中参数的矩估计方法

Copula函数是将多维随机变量的联合分布和其边缘分布连接起来的一种函数.关于Copula函数的理论和应用已有不同深度的研究,特别是Copula函数中未知参数的估计问题.本文研究了Gumbel Copula函数的参数估计,提出了矩估计和近似矩估计两种方法,分别得到了未知参数的估计结果,并通过模拟研究对这两种方法进行了比较,结果显示矩估计方法更为合理.