Adaptive Ridge Approach to Heteroscedastic Regression

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.