Scale-Space Methodology Applied to Spectral Feature Detection, Multinormality Testing and the k-sample Problem, and Wavelet Variance Analysis

The number of scale-space statistical algorithms has been greatly increased over the last 15 years. The concept originated from computer vision, introduced in Lindeberg (1994). The seminal paper by Chaudhuri and Marron (1999) brought the scale-space concept into smoothing of curves and kernel density estimation through the SiZer tool. By using all relevant smoothing bandwidths, i.e., the scale part, SiZer allows the user to look for interesting features in the smoothed curves or density estimates simultaneously on all bandwidths. In the years following, a number of classical statistical problems were also included in the family of scale-space algorithms. In this thesis, new scale-space algorithms for four such classical statistical problems are suggested. Paper II presents two closely related problems, addressed with highly similar approaches. Paper I addresses spectral scale-space analysis. Peaks found in the estimated spectral density function of evenly sampled stationary signals are typically of great interest for scientists. A peak found at a given frequency translates to potential (hidden) periodic