Semiparametric estimation of conditional heteroscedasticity via single-index modeling

We consider a single-index structure to study heteroscedasticity in regression with high-dimensional predictors. A general class of estimating equations is introduced. The resulting estimators remain consistent even when the structure of the variance function is misspecified. The proposed estimators estimate the conditional variance function asymptotically as well as if the conditional mean function was given a priori. Numerical studies confirm our theoretical observations and demonstrate that our proposed estimators have less bias and smaller standard deviation than the existing estimators.