  Recent methods for estimating sparse undirected graphs for real-valued data
in high dimensional problems rely heavily on the assumption of normality. We
show how to use a semiparametric Gaussian copula--or "nonparanormal"--for high
dimensional inference. Just as additive models extend linear models by
replacing linear functions with a set of one-dimensional smooth functions, the
nonparanormal extends the normal by transforming the variables by smooth
functions. We derive a method for estimating the nonparanormal, study the
method's theoretical properties, and show that it works well in many examples.
