B0228
Title: Post-model selection robust inference using empirical divergence statistics in ultra-high dimensional problems
Authors: Anand Vidyashankar - George Mason University (United States) [presenting]
Abstract: High dimensional data are ubiquitous in contemporary science and regression type models are typically used to address related inferential questions. A strategy, typically adopted by practicing statisticians is to first perform ``exploratory analyses'' and use model selection criteria such as BIC/GCV to select an appropriate model. The chosen model then gets treated as a ``true model'' and further inferences are performed. More recently, methods such as LASSO/ALASSO/SCAD/MCP and their variants also get used towards simultaneous variable selection and inference. It is now folklore that such a strategy towards inference may lead to inaccurate standard errors for the estimates of the regression parameters, potentially leading to erroneous decision making; also, additional complications arise if the underlying statistical model is misspecified. We provide a new framework, using divergences and empirical likelihood, to assess model selection variability and identify two important sub-components: namely, intrinsic and extrinsic uncertainty. We evaluate the effect of these sub-components on the robustness and efficiency of inference.
