Minimax A- and D-optimal Integer-Valued Wavelet Designs for Estimation Abbreviated title: Minimax A- and D-optimal Wavelet Designs

نویسنده

  • Alwell J. Oyet
چکیده

In this study we discuss integer-valued designs for wavelet estimation of nonparametric response curves in the possible presence of heteroscedastic noise based on a modi ̄ed wavelet version of the Gasser-MÄ uller kernel estimator and weighted least squares estimation. The Gasser-MÄ uller estimator was modi ̄ed in order to obtain an exact expression for the bias of the estimator. We ̄rst use data simulated from three curves to demonstrate that these estimators are °exible enough to e®ectively estimate nonparametric curves. Then, using a minimax treatment and the simulated annealing algorithm, we construct integer-valued designs for wavelet estimation of nonparametric curves. We present some examples involving the Daubechies and the multiwavelet systems. We discuss designs for three case studies on an experiment to investigate Gompertz theory, nitrite utilization in bush beans and the motorcycle impact experiment.

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تاریخ انتشار 2001