Abstract:
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Model selection has an important role in modern statistical analysis. Although BIC is derived by applying Laplace's method to the log-marginal likelihood functions, to show the validity of the approximations, we usually assume that a class of parametric models includes a correctly specified model. Lv and Liu (2014, Journal of the Royal Statistical Society Series B 76, 141-167) derive valid asymptotic expansions for the marginal likelihood functions in misspecified GLMs under some reasonable conditions, and propose the generalized BIC. In this talk, we derive a higher-order asymptotic expansion for the marginal likelihood functions under conditions similar to those of Lv and Liu, and present an alternative BIC criterion. However, we need a continuity condition on the prior density, which is stronger than that of Lv and Liu. We also present several numerical examples to illustrate the finite-sample performance of the alternative BIC in both correctly specified and misspecified logistic models.
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