  We consider the high-dimensional heteroscedastic regression model, where the
mean and the log variance are modeled as a linear combination of input
variables. Existing literature on high-dimensional linear regres- sion models
has largely ignored non-constant error variances, even though they commonly
occur in a variety of applications ranging from biostatis- tics to finance. In
this paper we study a class of non-convex penalized pseudolikelihood estimators
for both the mean and variance parameters. We show that the Heteroscedastic
Iterative Penalized Pseudolikelihood Optimizer (HIPPO) achieves the oracle
property, that is, we prove that the rates of convergence are the same as if
the true model was known. We demonstrate numerical properties of the procedure
on a simulation study and real world data.
