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Goodness-of-fit tests for noisy directional data

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The spherical convolution model provides a setup where each genuine observation Xi belonging to S2 the unit sphere of R3, is contaminated by a small random rotation. The aim of the present work is to provide nonparametric adaptive minimax goodness-of-fit testing procedures on f, the density of Xi from noisy observations. More precisely, let f0 being the uniform density on S2, we consider the problem of testing the the null hypothesis f = f0 with alternatives expressed in L2 norm over Sobolev class.

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