Masters in Statistics Oral Defense: "On Post-Selection Confidence Intervals in Linear Regression"

Abstract: The general goal of this thesis is to investigate and examine some issues about post-selection inference which arises from the setting where statistical inference is carried out after a data- driven model selection step. In this setting, the classical inference theory which requires a fixed priori model becomes invalid since the selected model is a result of random event. Hence, a common practice in applied research which ignores the model selection and builds up confidence interval will result in misleading or even false conclusion. In this thesis, specifically, we first discusses some examples to show how the classical inference theory loses efficacy after selection. Then we focus on the scenario of linear regression, and review two different interpretation views of parameters, i.e., full model view and and submodel view. We study the simultaneous post-selection inference solution under submodel view provided by Berk et al. [Ann. Stat. 41 (2013) 802-837] and carry out simulation to examine the results of Leeb et al. [Stat. Sci. 30 (2015) 216-227].

Host: Todd Kuffner