Doubly penalized likelihood estimator in heteroscedastic regression

A penalized likelihood estimation procedure is developed for heteroscedastic regression. A distinguishing feature of the new methodology is that it estimates both the mean and variance functions simultaneously without parametric assumption for either. An efficient implementation of the estimating procedure is also provided. The procedure is illustrated by a Monte Carlo example. A potential generalization, and application to the covariance modeling problem in numerical weather prediction is noted.