Integer-Valued Designs and Wavelet Versions of Nonparametric Curve Estimators Abbreviated title: Wavelet Curve Estimation

In this article, we discuss wavelet versions of nonparametric curve estimators and weighted least squares wavelet regression. We introduce a modi ̄ed wavelet version of the Gasser-MÄ uller estimator that is unbiased whenever a wavelet representation of the nonparametric response curve correctly speci ̄es the response. In some cases, involving the Daubechies wavelet system, we ̄nd that the modi ̄ed version estimates the response curve more closely than the Gasser-MÄ uller estimator. We use the modi ̄ed wavelet version to construct integer-valued designs for estimating nonparametric curves based on simulated annealing. Our study involves the Haar, Daubechies and the multiwavelet systems. We present some illustrative examples based on simulated data.