Wavelet estimations of the derivatives of variance function in heteroscedastic model

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 $L^{\tilde{p}}(1\le \tilde{p}<\mathrm{\infty })$ 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.