Bitte verwenden Sie diesen Link, um diese Publikation zu zitieren, oder auf sie als Internetquelle zu verweisen: https://hdl.handle.net/10419/25016 
Erscheinungsjahr: 
2007
Schriftenreihe/Nr.: 
Technical Report No. 2007,33
Verlag: 
Universität Dortmund, Sonderforschungsbereich 475 - Komplexitätsreduktion in Multivariaten Datenstrukturen, Dortmund
Zusammenfassung: 
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 e±cient 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.
Schlagwörter: 
Chebyshev polynomials
direct estimation
minimax designs
robust designs
series estimation
spherical harmonic descriptors
unbiased design
Zernike polynomials
Dokumentart: 
Working Paper

Datei(en):
Datei
Größe
271.12 kB





Publikationen in EconStor sind urheberrechtlich geschützt.