Exact minimax wavelet designs for discrimination

Abstract

In this thesis, we consider the problem of constructing designs in order to determine the number of wavelet terms that should be included in the wavelet representation of unknown nonparametric response curves. Our approach is to choose designs that will maximize, in some sense, the difference between the better model and the other competing wavelet models. Simulated annealing algorithm is developed to carry out exact, rather than approximate, minimax designs for discrimination between competing wavelet regression models. Sequential and nonsequential designs are discussed along with some examples based on the multiwavelet system and Daubechies wavelet system.