MAP Estimation Using a Possibly Misspecified Parameter Redundant Model

In this paper, new theorems are proved which show how in some cases the asymptotic distribution of Maximum A Posteriori (MAP) estimates can be obtained for parameter redundant probability models which are possibly misspecified. The new methods are then empirically investigated in a simulation study investigating confidence interval coverage for Cognitive Diagnostic Models (CDMs). The empirical results are shown to be relevant in the application of CDMs to small sample size situations.