A wavelet-based hybrid approach to estimate variance function in heteroscedastic regression models

We propose a wavelet-based hybrid approach to estimate the variance function in a nonparametric heteroscedastic fixed design regression model. A data-driven estimator is constructed by applying wavelet thresholding along with the technique of sparse representation to the difference-based initial estimates. We prove the convergence of the proposed estimator. The numerical results show that the proposed estimator performs better than the existing variance estimation procedures in the mean square sense over a range of smoothness classes.