Exact prior‐free probabilistic inference in a class of non‐regular models
Ryan Martin, Yi Lin · Stat · 2016
Standard statistical methods, such as maximum likelihood, are often justified based on their asymptotic properties. For suitably regular models, this theory is standard, but when the model is non‐regular, for example, the support depends on the parameter, these asymptotic properties may be difficult to assess. Recently, an inferential model (IM) framework has been developed that provides valid prior‐free probabilistic inference without the need for asymptotic justification. In this paper, we construct an IM for a class of highly non‐regular models with parameter‐dependent support. This construction requires conditioning, which is facilitated through solving a particular differential equation. We prove that the plausibility intervals derived from this IM are exact, and we demonstrate, via simulations, that their exactness does not come at the cost of loss of efficiency. Copyright © 2016 John Wiley & Sons, Ltd.