The Annals of Statistics

Spatial adaption for predicting random functions

Thomas Müller-Gronbach and Klaus Ritter

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We study integration and reconstruction of Gaussian random functions with inhomogeneous local smoothness. A single realization may only be observed at a finite sampling design and the correct local smoothness is unknown. We construct adaptive two-stage designs that lead to asymptotically optimal methods. We show that every nonadaptive design is less efficient.

Article information

Ann. Statist., Volume 26, Number 6 (1998), 2264-2288.

First available in Project Euclid: 21 June 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62M20 62L03
Secondary: 60G15 60G25

Reconstruction integral estimation spatial adaption asymptotically optimal designs unknown smoothness nonparametric model


Müller-Gronbach, Thomas; Ritter, Klaus. Spatial adaption for predicting random functions. Ann. Statist. 26 (1998), no. 6, 2264--2288. doi:10.1214/aos/1024691470.

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