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Fully data-driven nonparametric variance estimators. (English) Zbl 0811.62047
Summary: We consider the problem of estimating the unknown variance function $$v$$ in a nonparametric regression model. As a basis for our estimators we take estimated residuals which are based on a kernel estimator of the mean vector. Then we form with these residuals a kernel estimator of $$v$$. Main emphasis is on a data-driven choice of the bandwidths involved in the procedure. It is shown that the risk of this estimator attains the uniform convergence rate in Sobolev classes for $$v$$ under weak smoothness assumptions on the mean. Moreover, we prove that there is asymptotically no loss due to the estimation of the mean.

##### MSC:
 62G07 Density estimation 62G20 Asymptotic properties of nonparametric inference
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