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 non stationary cases at the same time. The main point, however, is to compare to a Bayesian analysis of the same problem. A non informative 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 non-informative 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.

翻译：本研究将置信分布的概念应用于对一个简单自回归模型中的参数推断，该参数可以取值为1。这使得可以同时比较在平稳和非平稳情况下的渐近逼近。然而，主要是与同样问题的贝叶斯分析进行比较。对于一个参数，按照Jeffreys的定义，一个非信息性先验被给定为置信密度与似然比之比。通过这种方式，利用了置信和非信息性贝叶斯框架之间的相似性。结果表明，在平稳情况下，渐近地所启发的先验是平的。然而，如果允许一个单位参数，则该先验必须具有某个大小的1号尖峰。模拟研究和两个实际例子说明了这些想法。