Parametrization of closed surfaces for 3-D shape description
Computer Vision and Image Understanding
IEEE Transactions on Pattern Analysis and Machine Intelligence
Robust Rotation Angle Estimator
IEEE Transactions on Pattern Analysis and Machine Intelligence
On the recovery of a function on a circular domain
IEEE Transactions on Information Theory
ILr-optimal designs for a hierarchically ordered system of regression models
Computational Statistics & Data Analysis
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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.