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

Biedermann, Stefanie and Dette, Holger, (2001) Minimax optimal designs for nonparametric regression: a further optimality property of the uniform distribution Atkinson, Anthony C., Hackl, Peter and Müller, Werner G. (eds.) In MODA6: Advances in Model-Oriented Design and Analysis. Proceedings of the 6th International Workshop on Model-Oriented Design and Analysis held in Puchberg/Schneeberg, Austria, June 25-29, 2001. Physica-Verlag., pp. 13-20.

Record type: Conference or Workshop Item (Paper)

Abstract

In the common nonparametric regression model y_i = g(t_i) + \sigma (t_i)\, \varepsilon_i,\,\, i = 1, \ldots , n with i.i.d. noise and nonrepeatable design points t_i 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,\sigma). The minimax designs are found explicitly, and for certain special cases the optimality of the uniform distribution can be established.

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More information

Published date: 2001
Venue - Dates: 6th International Workshop on Model-Oriented Design and Analysis, 2001-06-25 - 2001-06-29
Keywords: nonparametric regression, kernel estimation, locally optimal designs, minimax designs, mean squared error
Organisations: Statistics

Identifiers

Local EPrints ID: 41839
URI: http://eprints.soton.ac.uk/id/eprint/41839
ISBN: 3790814008
PURE UUID: 0b7a8e7f-b00f-4849-a45f-70ca0422097c

Catalogue record

Date deposited: 10 Oct 2006
Last modified: 17 Jul 2017 15:27

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Contributors

Author: Holger Dette
Editor: Anthony C. Atkinson
Editor: Peter Hackl
Editor: Werner G. Müller

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