Yilmaz Yildiz E, Lawless Jerald F
Prosserman Centre for Health Research, Samuel Lunenfeld Research Institute, Mount Sinai Hospital, Toronto, ON, Canada.
Lifetime Data Anal. 2011 Jul;17(3):386-408. doi: 10.1007/s10985-011-9192-2. Epub 2011 Jan 29.
Copula models for multivariate lifetimes have become widely used in areas such as biomedicine, finance and insurance. This paper fills some gaps in existing methodology for copula parameters and model assessment. We consider procedures based on likelihood and pseudolikelihood ratio statistics and introduce semiparametric maximum likelihood estimation leading to semiparametric versions. For cases where standard asymptotic approximations do not hold, we propose an efficient simulation technique for obtaining p-values. We apply these methods to tests for a copula model, based on embedding it in a larger copula family. It is shown that the likelihood and pseudolikelihood ratio tests are consistent even when the expanded copula model is misspecified. Power comparisons with two other tests of fit indicate that model expansion provides a convenient, powerful and robust approach. The methods are illustrated on an application concerning the time to loss of vision in the two eyes of an individual.
用于多变量寿命的Copula模型已在生物医学、金融和保险等领域广泛应用。本文填补了Copula参数和模型评估现有方法中的一些空白。我们考虑基于似然和伪似然比统计量的程序，并引入半参数最大似然估计以得到半参数版本。对于标准渐近近似不成立的情况，我们提出一种有效的模拟技术来获得p值。我们将这些方法应用于Copula模型的检验，即将其嵌入到一个更大的Copula族中。结果表明，即使扩展的Copula模型设定错误，似然和伪似然比检验也是一致的。与其他两种拟合优度检验的功效比较表明，模型扩展提供了一种方便、强大且稳健的方法。这些方法通过一个关于个体双眼视力丧失时间的应用进行了说明。
