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

Minimax optimal designs for nonparametric regression: a further optimality property of the uniform distribution
Minimax optimal designs for nonparametric regression: a further optimality property of the uniform distribution
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.
nonparametric regression, kernel estimation, locally optimal designs, minimax designs, mean squared error
3790814008
13-20
Physica-Verlag
Biedermann, Stefanie
fe3027d2-13c3-4d9a-bfef-bcc7c6415039
Dette, Holger
8c7b1c2e-3adc-45df-acfc-9e76509a228e
Atkinson, Anthony C.
Hackl, Peter
Müller, Werner G.
Biedermann, Stefanie
fe3027d2-13c3-4d9a-bfef-bcc7c6415039
Dette, Holger
8c7b1c2e-3adc-45df-acfc-9e76509a228e
Atkinson, Anthony C.
Hackl, Peter
Müller, Werner G.

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, Puchberg am Schneeberg, Austria, 2001-06-24 - 2001-06-28
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
ORCID for Stefanie Biedermann: ORCID iD orcid.org/0000-0001-8900-8268

Catalogue record

Date deposited: 10 Oct 2006
Last modified: 12 Dec 2021 03:35

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Contributors

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

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