Project #3 With Richard Lockhart

Inference Conditional on a Tuning Parameter Selected by Cross Validation

There are now many penalized methods for fitting linear models; examples include ridge regression, LASSO, and SCAD. The penalty may be thought of as a prior distribution for the unknown regression coefficients. These methods have a so-called tuning parameter that is often selected by cross-validation. Recent work by the supervisor and co-authors has led to methods for conditional inference after model selection for a fixed value of the tuning parameter. The goal of this project is to investigate use of these methods of conditional inference when cross-validation is used to pick the tuning parameter. 

In this project, we will investigate numerically this idea for conditional inference and try to draw conclusions about the usefulness of this tactic. The USRA student will:

1. Conduct a literature review finding papers that describe such penalized methods and seek out those with implementations in R or another high level language for statistical research and analysis.
2. Develop R code to implement the conditional inference procedures in question.
3. Investigate the limits on the size of models and data sets that can comfortably be handled in this way.