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The problem of estimating a probability density function f on the d−1-dimensional unit sphere Sd−1 from directional data using the needlet frame is considered. It is shown that the decay of needlet coefficients supported near a point x∈Sd−1 of a function f:Sd−1→ℝ depends only on local Hölder continuity properties of f at x. This is then used to show that the thresholded needlet estimator introduced...
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