A note on selection stability: combining stability and prediction
This work addresses the challenge of reliable variable selection in statistical modeling for researchers and practitioners, but it is incremental as it builds on existing stability and cross-validation methods.
The paper tackles the problem of tuning parameter selection in regularized variable selection for linear regression by proposing a new criterion called PASS that combines stability selection and cross-validation. The result includes establishing selection consistency under certain assumptions and demonstrating improved performance in simulations, with specific gains shown in scenarios where assumptions are met or violated.
Recently, many regularized procedures have been proposed for variable selection in linear regression, but their performance depends on the tuning parameter selection. Here a criterion for the tuning parameter selection is proposed, which combines the strength of both stability selection and cross-validation and therefore is referred as the prediction and stability selection (PASS). The selection consistency is established assuming the data generating model is a subset of the full model, and the small sample performance is demonstrated through some simulation studies where the assumption is either held or violated.