Structural adaptation in the density model

02/25/2020

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by   Lepski O. V., et al.

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This paper deals with non-parametric density estimation on ^2 from i.i.d observations. It is assumed that after unknown rotation of the coordinate system the coordinates of the observations are independent random variables whose densities belong to a Hölder class with unknown parameters. The minimax and adaptive minimax theories for this structural statistical model are developed.