  We consider the problem of graph estimation in a zero-inflated Gaussian
model. In this model, zero-inflation is obtained by double truncation (right
and left) of a Gaussian vector. The goal is to recover the latent graph
structure of the Gaussian vector with observations of the zero-inflated
truncated vector. We propose a two step estimation procedure. The first step
consists in estimating each term of the covariance matrix by maximising the
corresponding bivariate marginal log-likelihood of the truncated vector. The
second one uses the graphical lasso procedure to estimate the precision matrix
sparsity, which encodes the graph structure. We then state some theoretical
convergence results about the convergence rate of the covariance matrix and
precision matrix estimators. These results allow us to establish consistency of
our procedure with respect to graph structure recovery. We also present some
simulation studies to corroborate the efficiency of our procedure.
