University of Chicago - Department of Statistics
Many statistical models are defined in terms of polynomial constraints, or in terms of polynomial or rational parametrizations. Such algebraic models include, for instance, factor analysis and instrumental variable models, latent class models, and more generally, discrete and Gaussian graphical models with hidden variables. Statistical inference in hidden variable models is complicated by the fact that the models' parameter spaces are typically not smooth. This is the motivation for this talk that considers testing a null hypothesis with singularities in algebraic models. The focus will be on the large-sample asymptotic behavior of likelihood ratio and Wald tests.