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Nonparametric regression estimation based on spatially inhomogeneous data: minimax global convergence rates and adaptivity

Anestis AntoniadisMarianna PenskyTheofanis Sapatinas — 2014

ESAIM: Probability and Statistics

We consider the nonparametric regression estimation problem of recovering an unknown response function on the basis of spatially inhomogeneous data when the design points follow a known density with a finite number of well-separated zeros. In particular, we consider two different cases: when has zeros of a polynomial order and when has zeros of an exponential order. These two cases correspond to moderate and severe data losses, respectively. We obtain asymptotic (as the sample size increases)...

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