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\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

Innovative fractional derivative estimation of the pseudo-state for a class of fractional order linear systems

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