Asymptotic efficiency of the two-stage estimation method for copula-based models
Asymptotic efficiency of the two-stage estimation method for copula-based models
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DOI：
10.1016/j.jmva.2004.06.003
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发表时间：
2005-06-01
影响因子：
1.6
通讯作者：
Joe, H
中科院分区：
文献类型：
--
作者：
Joe, H
对于多变量Copula模型，最大似然是计算上困难的，一个两阶段的估计过程已经提出了以前的第一阶段涉及最大似然从单变量利润，第二阶段涉及最大似然的依赖参数与单变量参数保持固定从第一阶段。利用推断函数的理论，得到了两阶段估计量的渐近协方差矩阵的一个易于分析的分块矩阵。与极大似然估计相比，两阶段估计过程的渐近相对效率进行了研究。分析的独立Copula和Frechet上限的极限情况下，有助于确定共同的模式，在效率的依赖性在模型中的增加。对于Frechet上界，两阶段估计过程有时可以等价于单变量参数的极大似然估计。数值结果显示，一些模型，包括多元有序概率和二元极值分布，以表明离散和连续数据的渐近效率的典型水平。(c)2004爱思唯尔公司All rights reserved.
For multivariate copula-based models for which maximum likelihood is computationally difficult, a two-stage estimation procedure has been proposed previously; the first stage involves maximum likelihood from univariate margins, and the second stage involves maximum likelihood of the dependence parameters with the univariate parameters held fixed from the first stage. Using the theory of inference functions, a partitioned matrix in a form amenable to analysis is obtained for the asymptotic covariance matrix of the two-stage estimator. The asymptotic relative efficiency of the two-stage estimation procedure compared with maximum likelihood estimation is studied. Analysis of the limiting cases of the independence copula and Frechet upper bound help to determine common patterns in the efficiency as the dependence in the model increases. For the Frechet upper bound, the two-stage estimation procedure can sometimes be equivalent to maximum likelihood estimation for the univariate parameters. Numerical results are shown for some models, including multivariate ordinal probit and bivariate extreme value distributions, to indicate the typical level of asymptotic efficiency for discrete and continuous data. (c) 2004 Elsevier Inc. All rights reserved.