  We consider the problem of providing valid inference for a selected parameter
in a sparse regression setting. It is well known that classical regression
tools can be unreliable in this context due to the bias generated in the
selection step. Many approaches have been proposed in recent years to ensure
inferential validity. Here, we consider a simple alternative to data splitting
based on randomising the response vector, which allows for higher selection and
inferential power than the former and is applicable with an arbitrary selection
rule. We provide a theoretical and empirical comparison of both methods and
extend the randomisation approach to non-normal settings. Our investigations
show that the gain in power can be substantial.
