Minimax optimal designs for nonparametric regression - a further optimality property of the uniform distribution

Stefanie Biedermann and Holger Dette

No 2000,43, Technical Reports from Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen

Abstract: In the common nonparametric regression model y(i) = g(ti) + a (ti) ei , i=1….,n with i.i.d - noise and nonrepeatable design points ti we consider the problem of choosing an optimal design for the estimation of the regression function g. A minimax approach is adopted which searches for designs minimizing the maximum of the asymptotic integrated mean squared error_ where the maximum is taken over an appropriately bounded class of functions (g,a). The minimax designs are found explicitly and for certain special cases the optimality of the uniform distribution can be established.

Keywords: Nonparametric regression; kernel estimation; locally optimal designs; minimax designs; mean squared error (search for similar items in EconPapers)
Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:zbw:sfb475:200043

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