Confidence Distributions for the Autoregressive Parameter

The notion of confidence distributions is applied to inference about the parameter in a simple autoregressive model, allowing the parameter to take the value one. This makes it possible to compare to asymptotic approximations in both the stationary and the nonstationary cases at the same time. The main point, however, is to compare to a Bayesian analysis of the same problem. A noninformative prior for a parameter, in the sense of Jeffreys, is given as the ratio of the confidence density and the likelihood. In this way, the similarity between the confidence and noninformative Bayesian frameworks is exploited. It is shown that, in the stationary case, asymptotically the so induced prior is flat. However, if a unit parameter is allowed, the induced prior has to have a spike at one of some size. Simulation studies and two empirical examples illustrate the ideas.

将置信分布（confidence distributions）的概念应用于简单自回归模型的参数统计推断问题，允许模型参数取值为1。这使得可同时在平稳与非平稳两种情形下与渐近近似方法开展对比。不过本文的核心目标是将该方法与同一问题的贝叶斯分析进行对比。杰弗里斯（Jeffreys）意义下的参数无信息先验（noninformative prior），可由置信密度（confidence density）与似然（likelihood）的比值表示。借此可充分挖掘置信分布框架与无信息贝叶斯框架之间的相似性。研究表明，在平稳情形下，由此诱导得到的先验在渐近意义下呈平坦分布。但若允许参数取值为1（即单位根情形），则诱导得到的先验必须在1处存在一定规模的尖峰。仿真实验与两个实证案例可对上述研究思路进行验证与阐释。