Golden, R. M. (1995). Making correct statistical inferences using a wrong probability model. Journal of Mathematical Psychology, 39, 3-20.
Large sample methods for estimating the variance of parameter estimates for hypothesis-testing purposes (White, 1982) and statistical tests for model selection (Vuong, 1989) when the statistical model is wrong (i.e., misspecified) are reviewed. A parallel distributed processing (PDP) statistical model for analyzing categorical time series data is then proposed, and a theorem establishing when the quasi-maximum likelihood estimates of the model are unique is stated and proved. Analyses of Golden et al.'s (1993) categorical time-series data with respect to the proposed PDP model showed that White's asymptotic statistical theory yielded results which were more consistent with boot-strap estimates than classical methods of statistical inference.