  Penalized regression models are popularly used in high-dimensional data
analysis to conduct variable selection and model fitting simultaneously.
Whereas success has been widely reported in literature, their performances
largely depend on the tuning parameters that balance the trade-off between
model fitting and model sparsity. Existing tuning criteria mainly follow the
route of minimizing the estimated prediction error or maximizing the posterior
model probability, such as cross-validation, AIC and BIC. This article
introduces a general tuning parameter selection criterion based on a novel
concept of variable selection stability. The key idea is to select the tuning
parameters so that the resultant penalized regression model is stable in
variable selection. The asymptotic selection consistency is established for
both fixed and diverging dimensions. The effectiveness of the proposed
criterion is also demonstrated in a variety of simulated examples as well as an
application to the prostate cancer data.
