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On optimal data-based bandwidth selection in kernel density estimation. (English) Zbl 0733.62045

Summary: A bandwidth selection method is proposed for kernel estimation. This is based on the straightforward idea of plugging estimates into the usual asymptotic representation for the optimal bandwidth, but with two important modifications. The result is a bandwidth selector with the, by nonparametric standards, extremely fast asymptotic rate of convergence of \(n^{-{1\over2}}\), where \(n\to \infty\) denotes sample size. Comparison is given to other bandwidth selection methods, and small sample impact is investigated.

MSC:

62G07 Density estimation
62G20 Asymptotic properties of nonparametric inference
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