  Uniform convergence of empirical norms - empirical measures of squared
functions - is a topic which has received considerable attention in the
literature on empirical processes. The results are relevant as empirical norms
occur due to symmetrization. They also play a prominent role in statistical
applications. The contraction inequality has been a main tool but recently
other approaches have shown to lead to better results in important cases. We
present an overview including the linear (anisotropic) case, and give new
results for inner products of functions. Our main application will be the
estimation of the parental structure in a directed acyclic graph. As
intermediate result we establish convergence of the least squares estimator
when the model is wrong.
