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. In, Atkinson, Anthony C., Hackl, Peter and Müller, Werner G. (eds.) 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. 6th International Workshop on Model-Oriented Design and Analysis New York, USA, Physica-Verlag, 13-20. (Contributions to Statistics).

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Description/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.

Item Type: Book Section
ISBNs: 3790814008 (hardback)
Keywords: nonparametric regression, kernel estimation, locally optimal designs, minimax designs, mean squared error
Subjects: Q Science > QA Mathematics
H Social Sciences > HA Statistics
Divisions: University Structure - Pre August 2011 > School of Mathematics > Statistics
ePrint ID: 41839
Date Deposited: 10 Oct 2006
Last Modified: 27 Mar 2014 18:26
Publisher: Physica-Verlag
URI: http://eprints.soton.ac.uk/id/eprint/41839

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