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.)
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.
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.
Conference or Workshop Item
|Venue - Dates:
||6th International Workshop on Model-Oriented Design and Analysis, 2001-06-25 - 2001-06-29
||nonparametric regression, kernel estimation, locally optimal designs, minimax designs, mean squared error
||10 Oct 2006
||16 Apr 2017 18:57
|Further Information:||Google Scholar|
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