Abstract:
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Complex statistical models that have multiple sources of dependencies and variability in the observations are of primary importance in studying data from multiple disciplines. These include spatial, temporal, spatio-temporal, various mixed effects and other statistical models. Of special importance among such models are those that are useful for studying problems where there is limited directly observed data, for example, as in small area models.
In this talk we first present a new resampling-based method that can be used for simultaneous variable selection and inference in several complex models, including small area and other mixed effects models. Theoretical results justifying the proposed resampling schemes will be presented, followed by simulations and real data examples. We will demonstrate how to use the proposed resampling technique for testing hypothesis on whether particular complex features in the models are required or not. For example, for small area models on a spatial field, we may test the hypothesis that relatively simpler spatial patterns like isotropy or conditional autoregression may suffice in the presence of the covariates for both the fixed and random effect
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