Abstract

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 regression models has largely ignored nonconstant error variances, even though they commonly occur in a variety of applications ranging from biostatistics to finance. In this paper we study a class of nonconvex 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.