Using pseudometrics in kernel density estimation |
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Authors: | Sigve Hovda |
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Institution: | 1. Department of Computer and Information Science, Norwegian University of Science and Technology, Trondheim, Norway;2. Verdande Technology, Stiklestadveien 1, 7041 Trondheim, Norway |
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Abstract: | Common kernel density estimators (KDE) are generalised, which involve that assumptions on the kernel of the distribution can be given. Instead of using metrics as input to the kernels, the new estimators use parameterisable pseudometrics. In general, the volumes of the balls in pseudometric spaces are dependent on both the radius and the location of the centre. To enable constant smoothing, the volumes of the balls need to be calculated and analytical expressions are preferred for computational reasons. Two suitable parametric families of pseudometrics are identified. One of them has common KDE as special cases. In a few experiments, the proposed estimators show increased statistical power when proper assumptions are made. As a consequence, this paper describes an approach, where partial knowledge about the distribution can be used effectively. Furthermore, it is suggested that the new estimators are adequate for statistical learning algorithms such as regression and classification. |
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Keywords: | nonparametric density estimation semiparametric density estimation nonparametric regression nonparametric functional data analysis volume of ball in pseudometric space |
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