MAKING CORRECT STATISTICAL INFERENCES USING A WRONG PROBABILITY MODEL

Large sample methods for estimating the variance of parameter estimates for hypothesis-testing purposes and statistical test for model selection 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. Analysis of Golden et al.'s (1993, in the Proceedings of the 14th Annual Conference of the Cognitive Science Society (pp. 487-491). Hillsdale, NJ: Erlbaum) 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. (C) 1995 Academic Press, Inc.