Lee-Carter型年龄-周期和年龄-周期-队列模型的可识别性问题
Identifiability issues of age-period and age-period-cohort models of the Lee-Carter type
摘要：
死亡率建模的主要方法是李-卡特模型及其许多扩展。Lee-Carter模型及其许多扩展使用潜在过程进行预测。这些模型估计使用两个步骤的程序，导致不一致的看法的潜在变量。本文认为这些模型的可识别性问题的角度，承认从一开始就作为一个随机过程的潜变量。我们称这种观点为插件年龄段或插件年龄段队列模型。定义一个参数向量，其中包括这个过程的基本参数，而不是它的实现，我们调查的期望值和协方差的插件李卡特模型是可识别的。例如，可以看到，即使在估计过程的两个步骤中，我们在某种意义上都具有可识别性，它也不一定会延续到插入式模型。
英文摘要：
The predominant way of modelling mortality rates is the Lee-Carter model and its many extensions. The Lee-Carter model and its many extensions use a latent process to forecast. These models are estimated using a two-step procedure that causes an inconsistent view on the latent variable. This paper considers identifiability issues of these models from a perspective that acknowledges the latent variable as a stochastic process from the beginning. We call this perspective the plug-in age-period or plug-in age-period-cohort model. Defining a parameter vector that includes the underlying parameters of this process rather than its realisations, we investigate whether the expected values and covariances of the plug-in Lee-Carter models are identifiable. It will be seen, for example, that even if in both steps of the estimation procedure we have identifiability in a certain sense it does not necessarily carry over to the plug-in models.
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