Estimation of a common mean vector in bivariate meta-analysis under the FGM copula

We propose a bivariate Farlie–Gumbel–Morgenstern (FGM) copula model for bivariate meta-analysis, and develop a maximum likelihood estimator for the common mean vector. With the aid of novel mathematical identities for the FGM copula, we derive the expression of the Fisher information matrix. We also derive an approximation formula for the Fisher information matrix, which is accurate and easy to compute. Based on the theory of independent but not identically distributed (i.n.i.d.) samples, we examine the asymptotic properties of the estimator. Simulation studies are given to demonstrate the performance of the proposed method, and a real data analysis is provided to illustrate the method.     

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。     

SEMIPARAMETRIC ESTIMATION OF THE ERROR DISTRIBUTION IN MULTIVARIATE REGRESSION USING COPULAS

A semiparametric method is developed to estimate the dependence parameter and the joint distribution of the error term in the multivariate linear regression model. The nonparametric part of the method treats the marginal distributions of the error term as unknown, and estimates them using suitable empirical distribution functions. Then the dependence parameter is estimated by either maximizing a pseudolikelihood or solving an estimating equation. It is shown that this estimator is asymptotically normal, and a consistent estimator of its large sample variance is given. A simulation study shows that the proposed semiparametric method is better than the parametric ones available when the error distribution is unknown, which is almost always the case in practice. It turns out that there is no loss of asymptotic efficiency as a result of the estimation of regression parameters. An empirical example on portfolio management is used to illustrate the method.     

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.     

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.     

On the diversity score: a copula approach

ABSTRACT

For the rating process of Collateralized Debt Obligations', Moody's suggests the Diversity Score as a measure of diversification in the collateral pool. This measure is used in Moody's Binomial Expansion Technique to infer the probability of default and thus the expected Loss in the portfolio. In this paper, we examine the appropriateness of this approach to assess the reality of defaults using a copula approach and lower tail dependence.     

股指期货与现货指数收益率序列相关性研究——基于Copula函数的实证分析

沪深300股指期货推出后,其与沪深300指数的关系就引起投资者和研究者的关注。以沪深300指数和沪深300股指期货的日收益率数据为基础,运用Copula函数建立Copula-GARCH(1,1)-GED模型对两者进行相关性分析,结果表明:沪深300指数与股指期货收益率序列之间相关程度非常高,而通过比较秩相关系数的拟合情况,二元正态Copula函数更接近实际情况;在平方欧式距离的标准下,二元t-Copula模型能够更好地描述沪深300指数与沪深300股指期货日收益率序列的相关结构;两序列的尾部相关程度非常高,表明当股票市场大幅度波动时,沪深300指数与沪深300股指期货的相关程度显著提高。     

中国创业板和主板市场之间的相关结构分析——基于Copula函数的实证研究

了解创业板与主板市场间的关系,对于理解两个市场的互动关系以及证券组合的设计和风险评估至关重要。文章利用创业板指数、沪深300指数数据,借助ARMA-GARCH-Normal-Copula和ARMA-GARCH-T-Copula模型分析了创业板和主板之间的相关结构。研究表明:创业板市场的波动要大于主板市场,创业板和主板存在一定的正相关关系,并且存在非对称的尾部结构;在尾部(上尾和下尾)上,创业板对主板的变化反应比主板对创业板的变化反应更强。     

Some advances in the study of the compatibility of three bivariate copulas

Summary In this paper we study the problem of the compatibility of three bivariate copulas, i.e., we look for conditions which allow us to assure the existence of a three-copula whose two-dimensional margins are given. As a particular case, we seek conditions for two bivariate copulasC ₁ andC ₂ under whichC ₂[C₁ (x, y), z] is a three-copula. We specifically study the compatibility of the copulasM, W andII with other copulas both in general and in the particular case. We also study the compatibility of a two-copula with convex linear combinations of other two-copulas. Several examples illustrate the results obtained in each case, and some applications are given.