  Selection of important covariates and to drop the unimportant ones from a
high-dimensional regression model is a long standing problem and hence have
received lots of attention in the last two decades. After selecting the correct
model, it is also important to properly estimate the existing parameters
corresponding to important covariates. In this spirit, Fan and Li (2001)
proposed Oracle property as a desired feature of a variable selection method.
Oracle property has two parts; one is the variable selection consistency (VSC)
and the other one is the asymptotic normality. Keeping VSC fixed and making the
other part stronger, Fan and Lv (2008) introduced the strong oracle property.
In this paper, we consider different penalized regression techniques which are
VSC and classify those based on oracle and strong oracle property. We show that
both the residual and the perturbation bootstrap methods are second order
correct for any penalized estimator irrespective of its class. Most interesting
of all is the Lasso, introduced by Tibshirani (1996). Although Lasso is VSC, it
is not asymptotically normal and hence fails to satisfy the oracle property.
