Robust designs for series estimation
- 作者：Holger Dette ; Douglas P. Wiens
- 关键词：Copper ; Dinuclear ; Electrochemistry ; Catecholase
- 刊名：Computational Statistics and Data Analysis
- 出版年：2008
- 期刊代码：19_01679473
- 类别：cp
- 出版时间：15 May 2008
- 卷：52
- 期：9
- 页码：4305-4324
- 文件大小：829 K
摘要
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.