Bootstrap tuning in Gaussian ordered model selection (Q2414090)

To avoid overfitting or underfitting, algorithms for model selection are very important. The authors propose a procedure for linear regression with heteroscedastic Gaussian noise (that is assumed to be independent). The procedure is based on multiple pairwise tests and it selects the smallest model which is accepted when compared to all larger models. The authors prove an exponential bound for the difference of their procedure and the oracle estimator. As the variance covariance structure of the noise is unknown in practice, the authors suggest using the wild bootstrap with Gaussian multipliers. They show that this resampling method is consistent. The procedure is also evaluated in a simulations study about a nonparametric regression model. It shows that the bootstrap method has a similar performance as the procedure based on the knowledge of the variance structure.