Predictive stability criteria for penalty selection in linear models

Abstract Choosing a shrinkage method can be done by selecting penalty from list of pre-specified penalties or constructing based on the data. If for class linear models is given, we introduce predictive stability criterion data perturbation to select list. Simulation studies show that our identifies methods usually agree with existing literature and help explain heuristically when given expected perform well. preference construct customized problem, then propose technique genetic algorithms, again using criterion. We find that, in general, custom never performs worse than any commonly used there are cases reduces recognizable penalty. Since selection mathematically equivalent prior selection, also constructs priors. Our methodology allows us observe oracle property typically holds satisfy basic regularity conditions therefore not restrictive enough play direct role selection. In addition, methodology, immediately applied real problems, permits take model mis-specification into account.