Variable Selection for High-Dimensional Heteroscedastic Regression and Its Applications

We are examining variable selection in high-dimensional linear heteroscedastic models. Drawing inspiration from the connection between the linear heteroscedastic function and the interaction model, we develop a two-stage algorithm to identify the relevant variables in the model mentioned above. We demonstrate the selection consistency of our proposed two-stage method and highlight its efficacy through numerical simulations. Furthermore, we leverage our method to pinpoint defective tools during the semiconductor manufacturing process.