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Estimation of densities and derivatives of densities with directional data. (English) Zbl 1054.62033
Summary: Estimating the density function of a random vector taking values on the d-dimensional unit sphere is considered. Also the estimation of the Laplacian of the density and estimation of other types of derivatives is considered. Fast convergence rate theory is developed for pointwise, \(L_1\), and \(L_2\) error, extending some results of Hall, Watson and Cabrera (1987). It is also proved that asymptotically the plug-in method is as good as using the asymptotically optimal deterministic smoothing parameter sequence.

MSC:
62G07 Density estimation
62H11 Directional data; spatial statistics
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