A decision theoretic approach to wavelet regression on curves with a high number of regressors

Here we consider a possibly multivariate regression setting where data arise as curves and where the number of predictors greatly exceeds the number of observations. We present typical applications in spectral calibration. We employ wavelets and transform curves into sets of wavelet coefficients describing local features of the spectra. We then apply a Bayesian decision theory approach to select those coefficients that predict well the response. The method requires cost specifications and we employ cost functions that depend on the wavelet scale. Stochastic optimization methods are needed to find optimal subsets. We investigate both simulated annealing and genetic algorithms.