Robust designs for series estimation
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Date
2007-10-25T11:54:22Z
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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
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Keywords
Chebyshev polynomials, Direct estimation, Minimax designs, Robust designs, Series estimation, Spherical harmonic descriptors, Unbiased design, Zernike polynomials