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An automatic bandwidth selector for kernel density estimation. (English) Zbl 0764.62034

Summary: To select a proper bandwidth is a critical step in kernel density estimation. It is well known that the bandwidth selected by cross- validation has a large variability. This difficulty limits the applicability of cross-validation. To reduce the variability, we suggested modifying the sample characteristic function beyond some cut- off frequency in estimating the bias term of the mean integrated squared error.
It is proposed to select the cut-off frequency by a generalization of cross-validation. For smooth density functions, the asymptotic distribution of the bandwidth estimator based on the estimated cut-off frequency is obtained. The proposed bandwidth estimator has a relative convergence rate \(n^{-{1\over 2}}\), which is much faster than the rate \(n^{-1/10}\) for the bandwidth estimate selected by cross-validation. A modification which reduces the chance of selecting a large cut-off frequency is also suggested. In simulation studies, the advantages of the proposed procedures are clearly demonstrated. The procedures are also applied to some data sets.

MSC:

62G07 Density estimation
62G20 Asymptotic properties of nonparametric inference
62E20 Asymptotic distribution theory in statistics
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