Choosing a penalty for model selection in heteroscedastic regression

Understand

We consider the problem of choosing between several models in least-squares regression with heteroscedastic data.

• We prove that any penalization procedure is suboptimal when the penalty is a function of the dimension of the model, at least for some typical heteroscedastic model selection problems.
• In particular, Mallows' Cp is suboptimal in this framework.
• On the contrary, optimal model selection is possible with data-driven penalties such as resampling or $V$-fold penalties.