Abstract not found

– is a general procedure for estimating a lower bound for the number of components and for estimating their parameters in an additive regression model. The method consists of a series of steps: a preliminary step for separating the signal from the background followed by identification of local maxima up to a noise level-dependent threshold, estimation of the component parameters using an iterative algorithm, and detection of mixtures of components within one local maximum using hypothesis testing. The leading example is a nuclear magnetic resonance (NMR) experiment for protein structure determination. After applying a Fourier transform to the NMR signals, NMR frequency data are multiple-peak data, where each peak corresponds to one component in the additive regression model. In this example, the primary objective is accurate estimation of the location parameters. Key words and phrases: mixture regression model, tensor-product wavelet decomposition, noise level-dependent threshold, backfitting, mixture detection, nuclear magnetic resonance, protein structure determination.