Wavelet estimations of the derivatives of variance function in heteroscedastic model

Abstract

This paper studies nonparametric estimations of the derivatives $ r^{(m)}(x) $ of the variance function in a heteroscedastic model. Using a wavelet method, a linear estimator and an adaptive nonlinear estimator are constructed. The convergence rates under $ L^{\tilde{p}} (1\leq \tilde{p} < \infty) $ risk of those two wavelet estimators are considered with some mild assumptions. A simulation study is presented to validate the performances of the wavelet estimators.

Keywords

• nonparametric wavelet estimation
• derivative function
• heteroscedastic model
• $ l^{\tilde{p}} $ risk