Adaptive Ridge Approach to Heteroscedastic Regression

We propose an adaptive ridge (AR) estimation scheme for a heteroscedastic linear regression model with log-linear noise in data. We simultaneously estimate the mean and variance parameters, demonstrating 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. Aspects of application and possible generalizations are presented through simulations and real data examples.