Truncated regular vines in high dimensions with application to financial data

Using only bivariate copulas as building blocks, regular vine copulas constitute a flexible class of high‐dimensional dependency models. However, the flexibility comes along with an exponentially increasing complexity in larger dimensions. In order to counteract this problem, we propose using statistical model selection techniques to either truncate or simplify a regular vine copula. As a special case, we consider the simplification of a canonical vine copula using a multivariate copula as previously treated by Heinen & Valdesogo ( 2009 ) and Valdesogo ( 2009 ). We validate the proposed approaches by extensive simulation studies and use them to investigate a 19‐dimensional financial data set of Norwegian and international market variables. The Canadian Journal of Statistics 40: 68–85; 2012 © 2012 Statistical Society of Canada     

Polynomial approximation of nonlinear regression functions

In the present paper a nonlinear regression function is approximated by a polynomial estimator according to the expectation of the quadratic L ²-distance as risk is given. For special experimental designs with repeating experimental points this estimator coincides with the estimator by the method of the reproducing kernel.

Considerations about the relation for the sample size and the degree of the approximation polynomial and about the quadratic mean are given.     

基于Pair-Copula的社保基金投资组合风险测度研究

社保基金是社会保障事业健康发展的基石,风险管理是社保基金保值增值的关键问题之一。提出pair—copula—GARCH—EVT模型以测度社保基金投资组合风险,与传统的n维。copula—GARCH—EVT模型相比,该模型不仅考虑了维数的影响,而且还能灵活地选择copula的类型。实证研究发现,基于pair—cOpula—GARCH--EVT模型测度社保基金投资组合风险的准确性要高于传统的copuIa--GARCH--EVT模型。     

Stochastic comparisons of parallel and series systems with heterogeneous resilience-scaled components

By adding a resilience parameter to the scale model, a general distribution family called resilience-scale model is introduced including exponential, Weibull, generalized exponential, exponentiated Weibull and exponentiated Lomax distributions as special cases. This paper carries out stochastic comparisons on parallel and series systems with heterogeneous resilience-scaled components. On the one hand, it is shown that more heterogeneity among the resilience-scaled components of a parallel [series] system with an Archimedean [survival] copula leads to better [worse] performance in the sense of the usual stochastic order. On the other hand, the [reversed hazard] hazard rate order is established for two series [parallel] systems consisting of independent heterogeneous resilience-scaled components. The skewness and dispersiveness are also investigated for the lifetimes of two parallel systems consisting of independent heterogeneous and homogeneous [multiple-outlier] resilience-scaled components. Numerical examples are provided to illustrate the effectiveness of our theoretical findings. These results not only generalize and extend some known ones in the literature, but also provide guidance for engineers to assemble systems with higher reliability in practical situations.     

A bivariate geometric distribution allowing for positive or negative correlation

In this paper, we propose a new bivariate geometric model, derived by linking two univariate geometric distributions through a specific copula function, allowing for positive and negative correlations. Some properties of this joint distribution are presented and discussed, with particular reference to attainable correlations, conditional distributions, reliability concepts, and parameter estimation. A Monte Carlo simulation study empirically evaluates and compares the performance of the proposed estimators in terms of bias and standard error. Finally, in order to demonstrate its usefulness, the model is applied to a real data set.     

Matching a correlation coefficient by a Gaussian copula

A Gaussian copula is widely used to define correlated random variables. To obtain a prescribed Pearson correlation coefficient of ρ_x between two random variables with given marginal distributions, the correlation coefficient ρ_z between two standard normal variables in the copula must take a specific value which satisfies an integral equation that links ρ_x to ρ_z. In a few cases, this equation has an explicit solution, but in other cases it must be solved numerically. This paper attempts to address this issue. If two continuous random variables are involved, the marginal transformation is approximated by a weighted sum of Hermite polynomials; via Mehler’s formula, a polynomial of ρ_z is derived to approximate the function relationship between ρ_x and ρ_z. If a discrete variable is involved, the marginal transformation is decomposed into piecewise continuous ones, and ρ_x is expressed as a polynomial of ρ_z by Taylor expansion. For a given ρ_x, ρ_z can be efficiently determined by solving a polynomial equation.     

汉译佛经中的判断句研究

本文在已有判断句研究的背景下,着重介绍汉译佛经判断句的研究状况。主要包括两部分内容：一是利用佛典语料研究判断句,二是针对佛典语料判断句的研究。文中在评述相关研究成果的同时,提出了目前研究中的某些不足或值得注意的问题。     

A new generalized weighted Weibull distribution with decreasing,increasing, upside-down bathtub,N-shape and M-shape hazard rate

Recently, Domma et al. [An extension of Azzalinis method, J. Comput. Appl. Math. 278 (2015), pp. 37–47] proposed an extension of Azzalini's method. This method can attract readers due to its flexibility and ease of applicability. Most of the weighted Weibull models that have been introduced are with monotonic hazard rate function. This fact limits their applicability. So, our aim is to build a new weighted Weibull distribution with monotonic and non-monotonic hazard rate function. A new weighted Weibull distribution, so-called generalized weighted Weibull (GWW) distribution, is introduced by a method exposed in Domma et al. [13]. GWW distribution possesses decreasing, increasing, upside-down bathtub, N-shape and M-shape hazard rate. Also, it is very easy to derive statistical properties of the GWW distribution. Finally, we consider application of the GWW model on a real data set, providing simulation study too.     

Examination and visualisation of the simplifying assumption for vine copulas in three dimensions

Vine copulas are a highly flexible class of dependence models, which are based on the decomposition of the density into bivariate building blocks. For applications one usually makes the simplifying assumption that copulas of conditional distributions are independent of the variables on which they are conditioned. However this assumption has been criticised for being too restrictive. We examine both simplified and non‐simplified vine copulas in three dimensions and investigate conceptual differences. We show and compare contour surfaces of three‐dimensional vine copula models, which prove to be much more informative than the contour lines of the bivariate marginals. Our investigation shows that non‐simplified vine copulas can exhibit arbitrarily irregular shapes, whereas simplified vine copulas appear to be smooth extrapolations of their bivariate margins to three dimensions. In addition to a variety of constructed examples, we also investigate a three‐dimensional subset of the well‐known uranium data set and visually detect the fact that a non‐simplified vine copula is necessary to capture its complex dependence structure.     

Copula及其在贷款风险管理中的应用

相关性是贷款组合管理的关键性因素.本文介绍研究相关性的一种统一而灵活的工具--copula,并使用Monte Carlo仿真方法对高斯copula和t-copula进行比较,结果表明,t-copula对度量服从厚尾分布的贷款风险比高斯copula更精确.