CIM Seminar with Rolf Larsson

Abstract: At first, we will give a short historical overview of the development of statistical inference paradigms, where Bayesian methods came first (Laplace and others), and then frequentist (Fisher and others). Confidence distributions is a frequentist concept that tries to accomplish what Bayesian methods do, i.e. to give a probability distribution for a parameter. However, contrary to Bayesian methods, no prior distribution is needed.

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. The similarity between the confidence and non-informative Bayesian frameworks is exploited. It is shown that, in the stationary case, asymptotically a full analogy is obtained for a flat prior. However, if a unit parameter is allowed, for the analogy to hold there has to be a spike at one of some size in the prior.
Simulation studies and two empirical examples illustrate the ideas.
 

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