  We set up a formal framework to characterize encompassing of nonparametric
models through the L2 distance. We contrast it to previous literature on the
comparison of nonparametric regression models. We then develop testing
procedures for the encompassing hypothesis that are fully nonparametric. Our
test statistics depend on kernel regression, raising the issue of bandwidth's
choice. We investigate two alternative approaches to obtain a "small bias
property" for our test statistics. We show the validity of a wild bootstrap
method. We empirically study the use of a data-driven bandwidth and illustrate
the attractive features of our tests for small and moderate samples.
