Optimal designs for smoothing splines
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Date
2007-09-05T12:37:20Z
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Abstract
In the common nonparametric regression model we consider the problem of constructing
optimal designs, if the unknown curve is estimated by a smoothing spline. A new basis for
the space of natural splines is derived, and the local minimax property for these splines
is used to derive two optimality criteria for the construction of optimal designs. The first
criterion determines the design for a most precise estimation of the coefficients in the spline
representation and corresponds to D-optimality, while the second criterion is the G-criterion
and corresponds to an accurate prediction of the curve. Several properties of the optimal
designs are derived. In general D- and G-optimal designs are not equivalent. Optimal
designs are determined numerically and compared with the uniform design.
AMS Subject Classification: Primary 62K05; Secondary: 65D10
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Keywords
D- and G-optimal designs, Nonparametric regression, Saturated designs, Smoothing spline