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Predictive Assessment of Model Uncertainty
Abstract
In this dissertation, we use several predictive approaches to address the problem of model selection uncertainty. Unless a data generator is known a priori, there is uncertainty associated with model selection in any statistical analysis. We present three related, but different predictive methods that handle model uncertainty in dif- ferent ways. The first approach uses predictive stability in response to perturbing the data to choose a robust model from a pre-specified list. Here we focus on shrinkage methods used in a high dimensional regression setting, but note that our predictive stability criteria can be used for generic lists of pre-specified models. The second approach uses model averaging techniques to obtain a predictive distribution that accounts for all sources of uncertainty stemming from modeling choices made by an analyst. Our main contribution comes from defining a finite dimensional discrete random variable to decompose the predictive variance into portions representing com- ponents of the modeling procedure. The terms in the decomposition are analogous to the terms in Cochran’s theorem decomposition used in ANOVA. Each term in the decomposition is distributed like a weighted chi-square, but exact distributions are not available. Hence, we also present a bootstrap testing procedure that allows us to to determine if a component of the modeling strategy significantly contributes to the predictive variance. The third approach gives asymptotically valid predictive intervals for GLM’s, as well a small sample cross validation and bootstrap predictive intervals when asymptotic results cannot be assumed.
Subject Area
Statistics
Recommended Citation
Dustin, Dean, "Predictive Assessment of Model Uncertainty" (2022). ETD collection for University of Nebraska-Lincoln. AAI29996077.
https://digitalcommons.unl.edu/dissertations/AAI29996077