Abstract: 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 and phrases: Fractional Brownian motion, fractional Gaussian noise, inverse problem, jump, sharp cusp, vaguelette, wavelet-vaguelette decomposition.