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Short Communications

An asymptotically minimax regression estimator in the uniform norm up to exact constant

A. P. Korostelev

Institute for System Research, Russian Academy of Sciences

Abstract: We study the asymptotic behavior of the minimax risk in nonparametric regression estimation in the uniform norm in classes of functions, satisfying the Lipschitz or Holder condition. For an arbitrary loss function, the exact asymptotic behavior of the risk under equidistant observation design and Gaussian noise is found.

Keywords: nonparametric regression, minimax risk, exact asymptotic behavior, uniform norm.

Received: 30.01.1990

 English version: Theory of Probability and its Applications, 1993, 38:4, 737–743

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