Authors: Dette, Holger
Wiens, Douglas P.
Title: Robust designs for series estimation
Language (ISO): en
Abstract: We discuss optimal design problems for a popular method of series estimation in regression problems. Commonly used design criteria are based on the generalized variance of the estimates of the coefficients in a truncated series expansion and do not take possible bias into account. We present a general perspective of constructing robust and efficient designs for series estimators which is based on the integrated mean squared error criterion. A minimax approach is used to derive designs which are robust with respect to deviations caused by the bias and the possibility of heteroscedasticity. A special case results from the imposition of an unbiasedness constraint; the resulting “unbiased designs” are particularly simple, and easily implemented. Our results are illustrated by constructing robust designs for series estimation with spherical harmonic descriptors, Zernike polynomials and Chebyshev polynomials. Primary 62K05; secondary 62J05
Subject Headings: Chebyshev polynomials
Direct estimation
Minimax designs
Robust designs
Series estimation
Spherical harmonic descriptors
Unbiased design
Zernike polynomials
Issue Date: 2007-10-25T11:54:22Z
Appears in Collections:Sonderforschungsbereich (SFB) 475

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