Dependence Calibration in Conditional Copulas: A Nonparametric Approach
Dependence Calibration in Conditional Copulas: A Nonparametric Approach
复制标题
DOI：
10.1111/j.1541-0420.2010.01472.x
复制
发表时间：
2011-06
期刊：
影响因子：
1.9
通讯作者：
Elif F. Acar;Radu V. Craiu;Fang Yao
中科院分区：
文献类型：
--
作者：
Elif F. Acar;Radu V. Craiu;Fang Yao
随机变量之间的相关性研究是统计学的主要内容。在许多情况下，两个或多个随机变量之间的依赖强度根据测量的协变量的值而变化。我们使用一个条件copula模型对这种类型的变化进行了推断，其中copula函数属于参数copula族，并且copula参数随协变量而变化。为了估计copula参数与协变量之间的函数关系，我们提出了一种基于局部似然的非参数方法。选择最能代表给定数据集的copula族也很重要。所提出的框架自然导致了一种基于交叉验证预测误差的新的copula选择方法。我们推导了得到的局部多项式估计量的渐近偏差和方差，并概述了如何构造逐点置信区间。我们的方法的有限样本性能通过模拟研究进行了研究，并使用匹配多胎数据的子集进行了说明。
Summary The study of dependence between random variables is a mainstay in statistics. In many cases, the strength of dependence between two or more random variables varies according to the values of a measured covariate. We propose inference for this type of variation using a conditional copula model where the copula function belongs to a parametric copula family and the copula parameter varies with the covariate. In order to estimate the functional relationship between the copula parameter and the covariate, we propose a nonparametric approach based on local likelihood. Of importance is also the choice of the copula family that best represents a given set of data. The proposed framework naturally leads to a novel copula selection method based on cross‐validated prediction errors. We derive the asymptotic bias and variance of the resulting local polynomial estimator, and outline how to construct pointwise confidence intervals. The finite‐sample performance of our method is investigated using simulation studies and is illustrated using a subset of the Matched Multiple Birth data.