Likelihood for Statistically Equivalent Models
Abstract: In likelihood inference we usually assume the model is fixed and then base inference on the corresponding likelihood function. Often however the choice of model is rather arbitrary, and there may be other models which fit the data equally well. We study robustness of likelihood inference over such “statistically equivalent” models, and suggest a simple “envelope likelihood” to capture this aspect of model uncertainty. Robustness depends critically on how we specify the parameter of interest. Some asymptotic theory is presented, illustrated by three examples.
Keywords: Likelihood inference, robust likelihood, model uncertainty, parameter of interest.