Technical Report // Sonderforschungsbereich 475, Komplexitätsreduktion in Multivariaten Datenstrukturen, Universität Dortmund 2007,33
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.
Chebyshev polynomials direct estimation minimax designs robust designs series estimation spherical harmonic descriptors unbiased design Zernike polynomials