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：置信分布的概念被应用于简单自回归模型中的参数推断，允许参数取值为1。这使得可以同时比较平稳与非平稳情形下的渐近近似。然而，主要目的在于与同一问题的贝叶斯分析进行比较。本文给出了杰弗里斯意义下的参数无信息先验，该先验表示为置信密度与似然函数之比。通过这种方式，利用了置信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，由此导出的先验渐近趋于平坦。然而，若允许单位参数的存在，该诱导先验必须在1处具有一定大小的尖峰。模拟研究与两个实证例子说明了这些观点。