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Central limit theorem for asymmetric kernel functionals. (English) Zbl 1095.62041
Summary: Asymmetric kernels are quite useful for the estimation of density functions with bounded support. Gamma kernels are designed to handle density functions whose supports are bounded from one end only, whereas beta kernels are particularly convenient for the estimation of density functions with compact support. These asymmetric kernels are nonnegative and free of boundary bias. Moreover, their shape varies according to the location of the data point, thus also changing the amount of smoothing. This paper applies the central limit theorem for degenerate U-statistics to compute the limiting distribution of a class of asymmetric kernel functionals.

62G07 Density estimation
60F05 Central limit and other weak theorems
62G20 Asymptotic properties of nonparametric inference
Full Text: DOI
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