Model search and inference by bootstrap \bumping"

We propose a bootstrap-based method for searching through a space of models. The technique is well suited to complex, adaptively tted models: it provides a convenient method for nding better local minima, for resistant tting, and for optimization under constraints. Applications to regression, classiication and density estimation are described. The collection of models can also be used to form a conn-dence set for the true underlying model, using a generalization of Efron's percentile interval. We also provide results on the asymptotic behaviour of bumping estimates.