CHANGE-POINTS VIA WAVELETS FOR INDIRECT DATA
Yazhen Wang · 1999
This article studies change-points of a function for noisy data observed from a transformation of the function. The proposed method uses a wavelet-vaguelette decomposition to extract information about the wavelet transformation of the function from the data and then detect and estimate change-points by the wavelet transformation. Asymptotic theory for the detection and estimation is established. A simulated example is carried out to illustrate the method. Key Words: Fractional Brownian motion, fractional Gaussian noise, inverse problem, jump, sharp cusp, vaguelette, wavelet-vaguelette decomposition. 1. Introduction Change-points describe sudden localized changes. The occurrence of change-points often reveal important information about the object under study, so there is a great interest in detecting and locating the change-points. Typical change-points for a general smooth function f(x) are isolated jumps and sharp cusps. We say function f has an ff (0 ff ! 1) sharp cusp at x 0 if ...