Cross-Fitted Residual Regression for High-Dimensional Heteroscedasticity Pursuit

There is a vast amount of work on high-dimensional regression. The common starting point for the existing theoretical to assume data generating model homoscedastic linear regression with some sparsity structure. In reality homoscedasticity assumption often violated, and hence understanding heteroscedasticity critical importance. this article we systematically study estimation heteroscedastic model. particular, emphasis how detect estimate effects reliably efficiently. To end, propose cross-fitted residual approach prove resulting estimator selection consistent establish its rates convergence. Our has tuning parameters be determined by in practice. We novel BIC parameter consistency. This first result under heteroscedasticity. analysis more involved order handle heteroscedasticity, develop couple interesting new concentration inequalities that are independent interests.