  We propose an adaptive ridge (AR) based estimation scheme for a
heteroscedastic linear model equipped with log-linear errors. We simultaneously
estimate the mean and variance parameters and show new asymptotic
distributional and tightness properties in a sparse setting. We also show that
estimates for zero parameters shrink with more iterations under suitable
assumptions for tuning parameters. We observe possible generalizations of this
paper's results through simulations and will apply the estimation method in
forecasting electricity consumption.
