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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.

62G07 Density estimation
62G20 Asymptotic properties of nonparametric inference
Full Text: DOI
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