Biedermann, Stefanie and Dette, Holger
Minimax optimal designs for nonparametric regression: a further optimality property of the uniform distribution.
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,
(Contributions to Statistics).
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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