Distribution-Free Changepoint Detection for Nonlinear Profiles

We consider changepoint detection in a process in which the observed points are profiles: large sets of functionally related points (x, y). Few changepoint detection methods have been proposed that don’t rely in some capacity on the assumption that the observational errors are normally distributed. In this paper, a nonparametric distribution-free wavelet method is proposed for monitoring for changes in sequences of nonlinear profiles. No assumptions are made on the nature or form of the changes between the profiles other than finite square-integrability and no distributional assumption is made on the noise. Using only the magnitudes and location maps of thresholded wavelet coefficients, our method uses the spatial adaptivity property of wavelets to accurately detect profile changes when the signal is obscured with a variety of non-Gaussian errors. The efficiency of the proposed method, including comparisons to existing profile monitoring methods, is shown via simulation and applied to vertical density profile data.