JournalsmslVol. 3, No. 3/4pp. 345–386

Structural adaptation in the density model

  • Oleg V. Lepski

    Aix–Marseille Université, CNRS, France
  • Gilles Rebelles

    Lycée Jean Perrin, Marseille, France
Structural adaptation in the density model cover

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Abstract

This paper deals with nonparametric density estimation on R2\mathbb{R}^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.

Cite this article

Oleg V. Lepski, Gilles Rebelles, Structural adaptation in the density model. Math. Stat. Learn. 3 (2020), no. 3, pp. 345–386

DOI 10.4171/MSL/24